Recent zbMATH articles in MSC 45 https://www.zbmath.org/atom/cc/45 2022-06-24T15:10:38.853281Z Werkzeug On Hilfer generalized proportional fractional derivative https://www.zbmath.org/1485.26002 2022-06-24T15:10:38.853281Z "Ahmed, Idris" https://www.zbmath.org/authors/?q=ai:ahmed.idris "Kumam, Poom" https://www.zbmath.org/authors/?q=ai:kumam.poom "Jarad, Fahd" https://www.zbmath.org/authors/?q=ai:jarad.fahd "Borisut, Piyachat" https://www.zbmath.org/authors/?q=ai:borisut.piyachat "Jirakitpuwapat, Wachirapong" https://www.zbmath.org/authors/?q=ai:jirakitpuwapat.wachirapong Summary: Motivated by the Hilfer and the Hilfer-Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann-Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results. The Minkowski inequalities via generalized proportional fractional integral operators https://www.zbmath.org/1485.26026 2022-06-24T15:10:38.853281Z "Rahman, Gauhar" https://www.zbmath.org/authors/?q=ai:rahman.gauhar "Khan, Aftab" https://www.zbmath.org/authors/?q=ai:khan.aftab "Abdeljawad, Thabet" https://www.zbmath.org/authors/?q=ai:abdeljawad.thabet "Nisar, Kottakkaran Sooppy" https://www.zbmath.org/authors/?q=ai:sooppy-nisar.kottakkaran Summary: Recent research has gained more attention on conformable integrals and derivatives to derive the various type of inequalities. One of the recent advancements in the field of fractional calculus is the generalized nonlocal proportional fractional integrals and derivatives lately introduced by \textit{F. Jarad} et al. [Generalized fractional derivatives generated by a class of local proportional derivatives'', Eur. Phys. J. Spec. Top. 226, No. 18, 3457--3471 (2017; \url{doi:10.1140/epjst/e2018-00021-7})] comprising the exponential functions in the kernels. The principal aim of this paper is to establish reverse Minkowski inequalities and some other fractional integral inequalities by utilizing generalized proportional fractional integrals. Also, two new theorems connected with this inequality as well as other inequalities associated with the generalized proportional fractional integrals are established. On the mathematical model of Rabies by using the fractional Caputo-Fabrizio derivative https://www.zbmath.org/1485.34025 2022-06-24T15:10:38.853281Z "Aydogan, Seher Melike" https://www.zbmath.org/authors/?q=ai:aydogan.seher-melike "Baleanu, Dumitru" https://www.zbmath.org/authors/?q=ai:baleanu.dumitru-i "Mohammadi, Hakimeh" https://www.zbmath.org/authors/?q=ai:mohammadi.hakimeh "Rezapour, Shahram" https://www.zbmath.org/authors/?q=ai:rezapour.shahram Summary: Using the fractional Caputo-Fabrizio derivative, we investigate a new version of the mathematical model of Rabies disease. Using fixed point results, we prove the existence of a unique solution. We calculate the equilibrium points and check the stability of solutions. We solve the equation by combining the Laplace transform and Adomian decomposition method. In numerical results, we investigate the effect of coefficients on the number of infected groups. We also examine the effect of derivation orders on the behavior of functions and make a comparison between the results of the integer-order derivative and the Caputo and Caputo-Fabrizio fractional-order derivatives. Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions https://www.zbmath.org/1485.34026 2022-06-24T15:10:38.853281Z "Bachar, Imed" https://www.zbmath.org/authors/?q=ai:bachar.imed "Mâagli, Habib" https://www.zbmath.org/authors/?q=ai:maagli.habib "Eltayeb, Hassan" https://www.zbmath.org/authors/?q=ai:eltayeb.hassan Summary: We deal with the following Riemann-Liouville fractional nonlinear boundary value problem: $\begin{cases} \mathcal{D}^{\alpha}v(x)+f(x,v(x))=0, \quad 2< \alpha \leq 3, x\in (0,1), \\ v(0)=v^{\prime}(0)=v(1)=0. \end{cases}$ Under mild assumptions, we prove the existence of a unique continuous solution $$v$$ to this problem satisfying $\bigl\vert v(x) \bigr\vert \leq cx^{\alpha -1}(1-x)\quad\text{for all }x \in [0,1]\text{ and some }c>0.$ Our results improve those obtained by \textit{Y. Zou} and \textit{G. He} [Appl. Math. Lett. 74, 68--73 (2017; Zbl 1376.34014)]. On non-instantaneous impulsive fractional differential equations and their equivalent integral equations https://www.zbmath.org/1485.34035 2022-06-24T15:10:38.853281Z "Fernandez, Arran" https://www.zbmath.org/authors/?q=ai:fernandez.arran "Ali, Sartaj" https://www.zbmath.org/authors/?q=ai:ali.sartaj "Zada, Akbar" https://www.zbmath.org/authors/?q=ai:zada.akbar Summary: Real-world processes that display non-local behaviours or interactions, and that are subject to external impulses over non-zero periods, can potentially be modelled using non-instantaneous impulsive fractional differential equations or systems. These have been the subject of many recent papers, which rely on re-formulating fractional differential equations in terms of integral equations, in order to prove results such as existence, uniqueness, and stability. However, specifically in the non-instantaneous impulsive case, some of the existing papers contain invalid re-formulations of the problem, based on a misunderstanding of how fractional operators behave. In this work, we highlight the correct ways of writing non-instantaneous impulsive fractional differential equations as equivalent integral equations, considering several different cases according to the lower limits of the integro-differential operators involved. On a new class of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses https://www.zbmath.org/1485.34152 2022-06-24T15:10:38.853281Z "Mallika Arjunan, M." https://www.zbmath.org/authors/?q=ai:mallika-arjunan.m "Abdeljawad, Thabet" https://www.zbmath.org/authors/?q=ai:abdeljawad.thabet "Kavitha, V." https://www.zbmath.org/authors/?q=ai:kavitha.veeraruna|kavitha.velusamy "Yousef, Ali" https://www.zbmath.org/authors/?q=ai:yousef.ali-s|yousef.ali-a Summary: This manuscripts main objective is to examine the existence of piecewise-continuous mild solution of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions (ABFVFIDI) with non-instantaneous impulses (NII) in Banach space. Based on Martelli's fixed point theorem and $$\rho$$-resolvent operators, we develop the main results. An example is given to support the validation of the theoretical results achieved. Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation https://www.zbmath.org/1485.34196 2022-06-24T15:10:38.853281Z "Guerfi, Abderrahim" https://www.zbmath.org/authors/?q=ai:guerfi.abderrahim "Ardjouni, Abdelouaheb" https://www.zbmath.org/authors/?q=ai:ardjouni.abdelouaheb Summary: In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results. Some unexplored questions arising in linear viscoelasticity https://www.zbmath.org/1485.35050 2022-06-24T15:10:38.853281Z "Conti, Monica" https://www.zbmath.org/authors/?q=ai:conti.monica-c "Dell'Oro, Filippo" https://www.zbmath.org/authors/?q=ai:delloro.filippo "Pata, Vittorino" https://www.zbmath.org/authors/?q=ai:pata.vittorino Summary: We consider the abstract integrodifferential equation $\ddot{u}(t)+A\left[u(t)+\int\limits_0^\infty\mu(s)[u(t)-u(t-s)]ds\right]=0$ modeling the dynamics of linearly viscoelastic solids. The equation is known to generate a semigroup $$S(t)$$ on a certain phase space, whose asymptotic properties have been the object of extensive studies in the last decades. Nevertheless, some relevant questions still remain open, with particular reference to the decay rate of the semigroup compared to the decay of the memory kernel $$\mu$$, and to the structure of the spectrum of the infinitesimal generator of $$S(t)$$. This paper intends to provide some answers. Exponential attractors for the 3D fractional-order Bardina turbulence model with memory and horizontal filtering https://www.zbmath.org/1485.35068 2022-06-24T15:10:38.853281Z "Annese, Michele" https://www.zbmath.org/authors/?q=ai:annese.michele "Bisconti, Luca" https://www.zbmath.org/authors/?q=ai:bisconti.luca "Catania, Davide" https://www.zbmath.org/authors/?q=ai:catania.davide Summary: We consider the 3D simplified Bardina turbulence model with horizontal filtering, fractional dissipation, and the presence of a memory term incorporating hereditary effects. We analyze the regularity properties and the dissipative nature of the considered system and, in our main result, we show the existence of a global exponential attractor in a suitable phase space. Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian https://www.zbmath.org/1485.35304 2022-06-24T15:10:38.853281Z "Feulefack, Pierre Aime" https://www.zbmath.org/authors/?q=ai:feulefack.pierre-aime "Jarohs, Sven" https://www.zbmath.org/authors/?q=ai:jarohs.sven "Weth, Tobias" https://www.zbmath.org/authors/?q=ai:weth.tobias Summary: We study the asymptotics of Dirichlet eigenvalues and eigenfunctions of the fractional Laplacian $$(-\Delta)^s$$ in bounded open Lipschitz sets in the small order limit $$s \rightarrow 0^+$$. While it is easy to see that all eigenvalues converge to 1 as $$s \rightarrow 0^+$$, we show that the first order correction in these asymptotics is given by the eigenvalues of the logarithmic Laplacian operator, i.e., the singular integral operator with Fourier symbol $$2\log |\xi |$$. By this we generalize a result of Chen and the third author which was restricted to the principal eigenvalue. Moreover, we show that $$L^2$$-normalized Dirichlet eigenfunctions of $$(-\Delta)^s$$ corresponding to the $$k$$-th eigenvalue are uniformly bounded and converge to the set of $$L^2$$-normalized eigenfunctions of the logarithmic Laplacian. In order to derive these spectral asymptotics, we establish new uniform regularity and boundary decay estimates for Dirichlet eigenfunctions for the fractional Laplacian. As a byproduct, we also obtain corresponding regularity properties of eigenfunctions of the logarithmic Laplacian. Quantitative spectral analysis of electromagnetic scattering. II: Evolution semigroups and non-perturbative solutions https://www.zbmath.org/1485.35351 2022-06-24T15:10:38.853281Z "Zhou, Yajun" https://www.zbmath.org/authors/?q=ai:zhou.yajun Summary: We carry out quantitative studies on the Green operator $$\hat{\mathscr{G}}$$ associated with the Born equation, an integral equation that models electromagnetic scattering, building the strong stability of the evolution semigroup $$\{\exp (i\tau G\hat{\mathscr{G}})\vert\tau\geq 0\}$$ on polynomial compactness and the Arendt-Batty-Lyubich-Vũ theorem. The strongly-stable evolution semigroup inspires our proposal of a nonperturbative method to solve the light scattering problem and improve the Born approximation. For Part I, see [Quantitative spectral analysis of electromagnetic scattering. I: $$L^ 2$$ and Hilbert-Schmidt norm bounds'', Preprint, \url{arXiv:1007.4375}]. On the stability of Fourier phase retrieval https://www.zbmath.org/1485.42009 2022-06-24T15:10:38.853281Z "Steinerberger, Stefan" https://www.zbmath.org/authors/?q=ai:steinerberger.stefan Summary: Phase retrieval is concerned with recovering a function $$f$$ from the absolute value of its Fourier transform $$|\widehat{f}|$$. We study the stability properties of this problem in Lebesgue spaces. Our main results shows that $\|f-g\|_{L^2(\mathbb{R}^n)} \le 2\cdot \| |\widehat{f}| - |\widehat{g}| \|_{L^2(\mathbb{R}^n)} + h_f\Bigl(\|f-g\|_{L^p(\mathbb{R}^n)}\Bigr) + J(\widehat{f}, \widehat{g}),$ where $$1 \le p < 2$$, $$h_f$$ is an explicit nonlinear function depending on the smoothness of $$f$$ and $$J$$ is an explicit term capturing the invariance under translations. A noteworthy aspect is that the stability is phrased in terms of $$L^p$$ for $$1 \le p < 2$$: in this region $$L^p$$ cannot be used to control $$L^2$$, our stability estimate has the flavor of an inverse Hölder inequality. It seems conceivable that the estimate is optimal up to constants. Operators of Volterra convolution type in generalized Hölder spaces https://www.zbmath.org/1485.44004 2022-06-24T15:10:38.853281Z "Mamatov, Tulkin" https://www.zbmath.org/authors/?q=ai:mamatov.tulkin Boundedness results for convolution type operators in Hölder spaces are investigated. A brief introduction to Zygmund type estimates for the modulus of continuity and for fractional derivatives is given. In Section~2, Theorem~1 proves a Zygmund type estimate for the one-dimensional Volterra convolution type integral; cf.~(2.7). Zygmund type estimates are obtained for the mixed continuity modulus of some mixed convolution type integrals. Moreover, these types of estimates affect the nature of the modulus of continuity for mixed fractional integrals in Hölder spaces, as is represented in Section~3. Reviewer: Deshna Loonker (Jodhpur) Existence and uniqueness of solution for two-dimensional fuzzy Volterra-Fredholm integral equation https://www.zbmath.org/1485.45001 2022-06-24T15:10:38.853281Z "Vu, Ho" https://www.zbmath.org/authors/?q=ai:vu.ho "Dong, Le Si" https://www.zbmath.org/authors/?q=ai:dong.le-si Summary: In this work, we prove the existence and uniqueness of the solution for the two-dimensional fuzzy Volterra-Fredholm integral equation under some suitable conditions. Moreover, some properties of the solution are established. Uniqueness of the Hadamard-type integral equations https://www.zbmath.org/1485.45002 2022-06-24T15:10:38.853281Z "Li, Chenkuan" https://www.zbmath.org/authors/?q=ai:li.chengkuan Summary: The goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko's approach and Banach's contraction principle. We also present several examples for illustration of the main theorems. Generalized spherical mean value operators on Euclidean space https://www.zbmath.org/1485.45003 2022-06-24T15:10:38.853281Z "Okada, Yasunori" https://www.zbmath.org/authors/?q=ai:okada.yasunori "Yamane, Hideshi" https://www.zbmath.org/authors/?q=ai:yamane.hideshi The authors show that certain convolution equations can be seen as an extension of linear partial differential equations with certain coefficients. In the introduction, several citations confirm that such equations have various applications, as for example in the theory of holomorphic functions on convex domains. \textit{K.-L. Lim} [The spherical mean value operators on Euclidean and hyperbolic spaces. Medford, MA: Tufts University (PhD thesis) (2012)] proved that spherical mean value operators on Euclidean spaces are surjective convolution operators. In Section 2, the authors introduce the Neumann version of spherical mean value operators and its generalization. Convolution operators and distributions are defined as well. The next sections are devoted to the invertibility of distributions, the surjectivity of the Neumann mean value operator on the space of smooth functions and some other related topics. Reviewer: Deshna Loonker (Jodhpur) On the uniqueness of the solution to the Wiener-Hopf equation with probability kernel https://www.zbmath.org/1485.45004 2022-06-24T15:10:38.853281Z "Sgibnev, Mikhail Sergeyevich" https://www.zbmath.org/authors/?q=ai:sgibnev.mikhail-sergeevich The inhomogeneous generalised Wiener-Hopf equation is $z(x) = \int_{-\infty}^x z(x-y)\, F(dy) + f(x), \qquad x\geq 0,$ where $$z$$ is the unknown function, $$F$$ is a given probability distribution and $$f$$ is a known function. A distribution $$F$$ is called arithmetic if it is concentrated at a set $$\lambda \mathbb{Z}$$ (for some non-zero $$\lambda\in\mathbb{R}$$), otherwise it is called nonarithmetic. For a nonarithmetic $$F$$ with a finite positive mean $$\mu=\int_{\mathbb{R}} x \,F(dx)$$ the uniqueness of the solution is proven. The method is based on an elaborated von Neumann series expansion $$(I-\mathcal{F})^{-1}=\sum_0^{\infty} \mathcal{F}^n$$ for convolutions. An analogous result for a discrete case with arithmetic $$F$$ is discussed as well. Reviewer: Vladimir V. Kisil (Leeds) Radial symmetry of nonnegative solutions for nonlinear integral systems https://www.zbmath.org/1485.45005 2022-06-24T15:10:38.853281Z "Li, Zhenjie" https://www.zbmath.org/authors/?q=ai:li.zhenjie "Zhou, Chunqin" https://www.zbmath.org/authors/?q=ai:zhou.chunqin Summary: In this paper, we investigate the nonnegative solutions of the nonlinear singular integral system $\begin{cases} u_i(x) = \int_{\mathbb{R}^n}\frac{1}{|x-y|^{n-\alpha}|y|^{a_i}}f_i(u(y))dy, \quad x\in\mathbb{R}^n, \quad i = 1,2\dots,m,\\ 0<\alpha<n,\quad u(x) = (u_1(x),\dots,u_m(x)), \end{cases}$ where $$0<a_i/2<\alpha$$, $$f_i(u)$$, $$1\leq i\leq m$$, are real-valued functions, nonnegative and monotone nondecreasing with respect to the independent variables $$u_1, u_2 ,\dots , u_m$$. By the method of moving planes in integral forms, we show that the nonnegative solution $$u = (u_1,u_2,\dots,u_m)$$ is radially symmetric when $$f_i$$ satisfies some monotonicity condition. Investigating a class of generalized Caputo-type fractional integro-differential equations https://www.zbmath.org/1485.45006 2022-06-24T15:10:38.853281Z "Ali, Saeed M." https://www.zbmath.org/authors/?q=ai:ali.saeed-m "Shatanawi, Wasfi" https://www.zbmath.org/authors/?q=ai:shatanawi.wasfi-a "Kassim, Mohammed D." https://www.zbmath.org/authors/?q=ai:kassim.mohammed-dahan "Abdo, Mohammed S." https://www.zbmath.org/authors/?q=ai:abdo.mohammed-salem "Saleh, S." https://www.zbmath.org/authors/?q=ai:saleh.sina|saleh.sagvan|saleh.sahar-mohamad|saleh.s-q|saleh.saleh-a|saleh.shanti-faridah|saleh.shokrya|saleh.s-v|saleh.samera-m|saleh.sami|saleh.siti-hidayah-muhad|saleh.s-a|saleh.saad-j Summary: In this article, we prove some new uniqueness and Ulam-Hyers stability results of a nonlinear generalized fractional integro-differential equation in the frame of Caputo derivative involving a new kernel in terms of another function $$\psi$$. Our approach is based on Babenko's technique, Banach's fixed point theorem, and Banach's space of absolutely continuous functions. The obtained results are demonstrated by constructing numerical examples. Existence results for a coupled system of Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions https://www.zbmath.org/1485.45007 2022-06-24T15:10:38.853281Z "Alsaedi, Ahmed" https://www.zbmath.org/authors/?q=ai:alsaedi.ahmed "Albideewi, Amjad F." https://www.zbmath.org/authors/?q=ai:albideewi.amjad-f "Ntouyas, Sotiris K." https://www.zbmath.org/authors/?q=ai:ntouyas.sotiris-k "Ahmad, Bashir" https://www.zbmath.org/authors/?q=ai:ahmad.bashir.2 Summary: This paper is concerned with the existence and uniqueness of solutions for a coupled system of Liouville-Caputo-type fractional integro-differential equations with multi-point and sub-strip boundary conditions. The fractional integro-differential equations involve Caputo derivative operators of different orders and finitely many Riemann-Liouville fractional integral and non-integral type nonlinearities. The boundary conditions at the terminal position $$t=1$$ involve sub-strips and multi-point contributions. The Banach fixed point theorem and the Leray-Schauder alternative are used to establish our results. The obtained results are illustrated with the aid of examples. Weakly perturbed boundary-value problems for systems of integro-differential equations with impulsive action https://www.zbmath.org/1485.45008 2022-06-24T15:10:38.853281Z "Bondar, Ivanna" https://www.zbmath.org/authors/?q=ai:bondar.ivanna Summary: The weakly perturbed BVP's for impulsive integro-differential systems are considered. Under the assumption that the generating problem (for $$\varepsilon=0)$$ does not have solutions on the space $$W^1_2[a,b]$$ for some in homogeneity and using the Vishik-Lyusternik method, we establish conditions for the existence of solutions of these problems on the space $$D_2\left([a,b]\setminus \{\tau_i\}_I\right)$$ in the form of a Laurent series in powers of small parameter $$\varepsilon$$ with finitely many terms with negative powers of $\varepsilon$, and we suggest an algorithm of construction of these solutions. Existence of mild solution for mixed Volterra-Fredholm integro fractional differential equation with non-instantaneous impulses https://www.zbmath.org/1485.45009 2022-06-24T15:10:38.853281Z "Borah, Jayanta" https://www.zbmath.org/authors/?q=ai:borah.jayanta "Bora, Swaroop Nandan" https://www.zbmath.org/authors/?q=ai:bora.swaroop-nandan Authors' abstract: We establish a set of sufficient conditions for the existence of mild solution of a class of fractional mixed integro differential equation with not instantaneous impulses. The results are obtained by establishing two theorems by using semigroup theory, Banach fixed point theorem and Krasnoselskii's fixed point theorem. Two examples are presented to validate the results of the theorems. Reviewer: Ahmed M. A. El-Sayed (Alexandria) Solving integral equations by means of fixed point theory https://www.zbmath.org/1485.45010 2022-06-24T15:10:38.853281Z "Karapinar, E." https://www.zbmath.org/authors/?q=ai:karapinar.erdal "Fulga, A." https://www.zbmath.org/authors/?q=ai:fulga.andreea "Shahzad, N." https://www.zbmath.org/authors/?q=ai:shahzad.naseer "Roldán López de Hierro, A. F." https://www.zbmath.org/authors/?q=ai:roldan-lopez-de-hierro.antonio-francisco Summary: One of the most interesting tasks in mathematics is, undoubtedly, to solve any kind of equations. Naturally, this problem has occupied the minds of mathematicians since the dawn of algebra. There are hundreds of techniques for solving many classes of equations, facing the problem of finding solutions and studying whether such solutions are unique or multiple. One of the recent methodologies that is having great success in this field of study is the fixed point theory. Its iterative procedures are applicable to a great variety of contexts in which other algorithms fail. In this paper, we study a very general class of integral equations by means of a novel family of contractions in the setting of metric spaces. The main advantage of this family is the fact that its general contractivity condition can be particularized in a wide range of ways, depending on many parameters. Furthermore, such a contractivity condition involves many distinct terms that can be either adding or multiplying between them. In addition to this, the main contractivity condition makes use of the self-composition of the operator, whose associated theorems used to be more general than the corresponding ones by only using such mapping. In this setting, we demonstrate some fixed point theorems that guarantee the existence and, in some cases, the uniqueness, of fixed points that can be interpreted as solutions of the mentioned integral equations. Study of nonlocal boundary value problem for the Fredholm-Volterra integro-differential equation https://www.zbmath.org/1485.45011 2022-06-24T15:10:38.853281Z "Raslan, K. R." https://www.zbmath.org/authors/?q=ai:raslan.kamal-raslan "Ali, Khalid K." https://www.zbmath.org/authors/?q=ai:ali.khalid-karam "Ahmed, Reda Gamal" https://www.zbmath.org/authors/?q=ai:ahmed.reda-gamal "Al-Jeaid, Hind K." https://www.zbmath.org/authors/?q=ai:al-jeaid.hind-k "Abd-Elall Ibrahim, Amira" https://www.zbmath.org/authors/?q=ai:abd-elall-ibrahim.amira Summary: In this paper, the existence and uniqueness of the Fredholm-Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra-Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. Finally, we solve some examples numerically to show the accuracy of the proposed method. Well-posedness and stability for a Moore-Gibson-Thompson equation with internal distributed delay https://www.zbmath.org/1485.45012 2022-06-24T15:10:38.853281Z "Braik, Abdelkader" https://www.zbmath.org/authors/?q=ai:braik.abdelkader "Beniani, Abderrahmane" https://www.zbmath.org/authors/?q=ai:beniani.abderrahmane "Zennir, Khaled" https://www.zbmath.org/authors/?q=ai:zennir.khaled Summary: In this work, we consider the Moore-Gibson-Thompson equation with distributed delay. We prove, under an appropriate assumptions and a smallness conditions on the parameters $$\alpha$$, $$\beta$$, $$\gamma$$ and $$\mu$$, that this problem is well-posed and then by introducing suitable energy and Lyapunov functionals, the solution of (1) and (2) decays to zero as $$t$$ tends to infinity. $$C^\ast$$-algebra valued fuzzy normed spaces with application of Hyers-Ulam stability of a random integral equation https://www.zbmath.org/1485.45013 2022-06-24T15:10:38.853281Z "Chaharpashlou, R." https://www.zbmath.org/authors/?q=ai:chaharpashlou.reza "O'Regan, Donal" https://www.zbmath.org/authors/?q=ai:oregan.donal "Park, Choonkil" https://www.zbmath.org/authors/?q=ai:park.choonkil "Saadati, Reza" https://www.zbmath.org/authors/?q=ai:saadati.reza Summary: In this paper, we consider $$C^\ast$$-algebra valued fuzzy normed spaces. We study the random integral equation $$(\frac{1}{2c})\int_{x-cd}^{x+cd}u(\gamma, \tau, d_0) d \tau = u(\gamma, x, d)$$ which is related to the stochastic wave equation. In addition, using a $$C^\ast$$-algebra valued fuzzy controller function, we consider its $$C^\ast$$-algebra valued fuzzy Hyers-Ulam stability. On a unified integral operator for $$\phi$$-convex functions https://www.zbmath.org/1485.45014 2022-06-24T15:10:38.853281Z "Chel Kwun, Young" https://www.zbmath.org/authors/?q=ai:kwun.young-chel "Zahra, Moquddsa" https://www.zbmath.org/authors/?q=ai:zahra.moquddsa "Farid, Ghulam" https://www.zbmath.org/authors/?q=ai:farid.ghulam "Zainab, Saira" https://www.zbmath.org/authors/?q=ai:zainab.saira "Min Kang, Shin" https://www.zbmath.org/authors/?q=ai:kang.shin-min Summary: Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use $$\phi$$-convex functions for unified integral operators to obtain their upper bounds and upper and lower bounds for symmetric $$\phi$$-convex functions in the form of a Hadamard inequality. Also, for $$\phi$$-convex functions, we obtain bounds of different known fractional and conformable fractional integrals. The results of this paper are applicable to convex functions. Certain inequalities via generalized proportional Hadamard fractional integral operators https://www.zbmath.org/1485.45015 2022-06-24T15:10:38.853281Z "Rahman, Gauhar" https://www.zbmath.org/authors/?q=ai:rahman.gauhar "Abdeljawad, Thabet" https://www.zbmath.org/authors/?q=ai:abdeljawad.thabet "Jarad, Fahd" https://www.zbmath.org/authors/?q=ai:jarad.fahd "Khan, Aftab" https://www.zbmath.org/authors/?q=ai:khan.aftab "Nisar, Kottakkaran Sooppy" https://www.zbmath.org/authors/?q=ai:sooppy-nisar.kottakkaran Summary: In the article, we introduce the generalized proportional Hadamard fractional integrals and establish several inequalities for convex functions in the framework of the defined class of fractional integrals. The given results are generalizations of some known results. Measures of noncompactness and infinite systems of integral equations of Urysohn type in $$L^\infty (\mathfrak{G})$$ https://www.zbmath.org/1485.47076 2022-06-24T15:10:38.853281Z "Banaei, Shahram" https://www.zbmath.org/authors/?q=ai:banaei.shahram "Parvaneh, Vahid" https://www.zbmath.org/authors/?q=ai:parvaneh.vahid "Mursaleen, Mohammad" https://www.zbmath.org/authors/?q=ai:mursaleen.mohammad Summary: In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space $$L^\infty(\mathfrak{G})$$ (where $$\mathfrak{G}\subseteq\mathbb{R}^\omega)$$ are proved. We handle our obtained consequences to inquire the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example. Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions https://www.zbmath.org/1485.49014 2022-06-24T15:10:38.853281Z "Yang, He" https://www.zbmath.org/authors/?q=ai:yang.he "Zhao, Yanxia" https://www.zbmath.org/authors/?q=ai:zhao.yanxia Summary: In this paper, the existence of solutions and optimal state-control pair of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions in abstract spaces are investigated. By using the Krasnoselskii's fixed point theorem, we first prove the existence of mild solutions of the concerned problem. Then without the Lipschitz continuity of the nonlinearity, the existence of optimal state-control pair of control system governed by impulsive integro-differential evolution equations is presented by constructing minimizing sequences twice. An example is given as an application of the abstract results. Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions https://www.zbmath.org/1485.54045 2022-06-24T15:10:38.853281Z "Al-Qurashi, Maysaa" https://www.zbmath.org/authors/?q=ai:alqurashi.maysaa-m|al-qurashi.maysaa-mohamed "Shagari, Mohammed Shehu" https://www.zbmath.org/authors/?q=ai:shagari.mohammed-shehu "Rashid, Saima" https://www.zbmath.org/authors/?q=ai:rashid.saima "Hamed, Y. S." https://www.zbmath.org/authors/?q=ai:hamed.yasser-s "Mohamed, Mohamed S." https://www.zbmath.org/authors/?q=ai:mohamed.mohamed-salem|mohamed.mohamed-saied-emam|mohamed.mohamed-said|mohamed.mohamed-saad Summary: In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $$b$$-metric spaces are examined. A~few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $$(\alpha, \beta)$$-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein. Fixed point results of a generalized reversed $$F$$-contraction mapping and its application https://www.zbmath.org/1485.54046 2022-06-24T15:10:38.853281Z "Bashir, Shahid" https://www.zbmath.org/authors/?q=ai:bashir.shahid "Saleem, Naeem" https://www.zbmath.org/authors/?q=ai:saleem.naeem "Husnine, Syed Muhammad" https://www.zbmath.org/authors/?q=ai:husnine.syed-muhammad Summary: In this paper, we introduce the reversal of generalized Banach contraction principle and mean Lipschitzian mapping respectively. Secondly, we prove the existence and uniqueness of fixed points for these expanding type mappings. Further, we extend Wardowski's idea of $$F$$-contraction by introducing the reversed generalized $$F$$-contraction mapping and use our obtained result to prove the existence and uniqueness of its fixed point. Finally, we apply our results to prove the existence of a unique solution of a non-linear integral equation. Existence of a solution of fractional differential equations using the fixed point technique in extended $$b$$-metric spaces https://www.zbmath.org/1485.54049 2022-06-24T15:10:38.853281Z "Bota, Monica-Felicia" https://www.zbmath.org/authors/?q=ai:bota.monica-felicia "Guran, Liliana" https://www.zbmath.org/authors/?q=ai:guran.liliana Summary: The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended $$b$$-metric spaces. The considered operators are generalized $$\varphi$$-contractions and $$\alpha - \varphi$$ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator. Asymptotically compatible schemes for robust discretization of parametrized problems with applications to nonlocal models https://www.zbmath.org/1485.65058 2022-06-24T15:10:38.853281Z "Tian, Xiaochuan" https://www.zbmath.org/authors/?q=ai:tian.xiaochuan "Du, Qiang" https://www.zbmath.org/authors/?q=ai:du.qiang Asymptotic error expansion of the iterated superconvergent Nyström method for Urysohn integral equations https://www.zbmath.org/1485.65128 2022-06-24T15:10:38.853281Z "Allouch, C." https://www.zbmath.org/authors/?q=ai:allouch.chafik "Medbouhi, A." https://www.zbmath.org/authors/?q=ai:medbouhi.a "Sbibih, D." https://www.zbmath.org/authors/?q=ai:sbibih.driss "Tahrichi, M." https://www.zbmath.org/authors/?q=ai:tahrichi.mohamed Summary: For a nonlinear Urysohn integral equation with smooth kernel, a superconvergent Nyström method proposed recently in [\textit{C. Allouch} et al., Appl. Math. Comput. 218, No. 22, 10777--10790 (2012; Zbl 1278.65186)], based on an interpolatory projection onto a space of piecewise polynomials of degree $$\le r$$, is shown to have convergence of order $$4r$$ for its iterated version. In this paper, a general theorem dealing with asymptotic error expansion for the iterated superconvergent Nyström solution is proved. The Richardson extrapolation is then applied to obtain a more accurate solution of order $$4r+2$$. Numerical results are given to illustrate this improvement of the convergence order. A numerical method for solving nonlinear Volterra-Fredholm integral equations https://www.zbmath.org/1485.65129 2022-06-24T15:10:38.853281Z "Binh, Ngo Thanh" https://www.zbmath.org/authors/?q=ai:binh.ngo-thanh "Ninh, Khuat Van" https://www.zbmath.org/authors/?q=ai:ninh.khuat-van Summary: We introduce a numerical method for solving nonlinear Volterra-Fredholm integral equations. Our method consists of two steps. First, we define a discretized form of the integral equation by quadrature methods. We then propose an interative method, which is based on a hybrid of the method of contractive mapping and parameter continuation method, to solve the perturbed system of nonlinear equations obtained from discretization of the considered problem. Finally, some examples are given to demonstrate the validity and applicability of our method. A numerical method for proportional delay Volterra integral equations https://www.zbmath.org/1485.65130 2022-06-24T15:10:38.853281Z "Katani, R." https://www.zbmath.org/authors/?q=ai:katani.roghayeh Summary: In this paper we propose a numerical method for nonlinear second kind Volterra integral equations (VIEs) with (vanishing) proportional delays $$qt$$ ($$0<q<1$$). We shall present the existence and uniqueness of analytic solution for these type equations and then analyze the convergence and order of convergence of the proposed numerical method. The numerical method is based on the Romberg quadrature rule and will be shown that the order of the convergence is $$O(N^{-5})$$, where $$N$$ is number of the nodes in the time discretization. The theoretical results are then verified by numerical examples, also they are compared with some other numerical methods. Approximate solution of a singular integral equation of the first kind using Chebyshev polynomials with zero values at both endpoints of the integration interval https://www.zbmath.org/1485.65131 2022-06-24T15:10:38.853281Z "Khubezhty, Sh. S." https://www.zbmath.org/authors/?q=ai:khubezhty.shalva-solomonovich Summary: A singular integral equation of the first kind is considered on the integration interval $$[ - 1,1]$$. A solution with zero values at the endpoints of the interval is sought. The equations are discretized using Chebyshev polynomials of the second kind. The expansion coefficients of the unknown function in the Chebyshev polynomials of the second kind are obtained by solving systems of linear algebraic equations. The fact is taken into account that a unique solution of this equation vanishing at the endpoints of the integration interval exists under additional conditions on the kernels and the right-hand side. This additional condition is also discretized. The constructed computational scheme is justified by applying a function analysis method with the use of the general theory of approximate methods. The space of Hölder continuous functions with relevant norms is introduced. The differences between the norms of the singular and approximate operators are estimated. Under certain conditions, the existence and uniqueness of the solution to the approximate singular integral equation are proved, and the computational error is estimated. The order with which the remainder tends to zero is given. The proposed theory is verified using test examples, which show the efficiency of the method. A novel collocated-shifted Lucas polynomial approach for fractional integro-differential equations https://www.zbmath.org/1485.65132 2022-06-24T15:10:38.853281Z "Koundal, Reena" https://www.zbmath.org/authors/?q=ai:koundal.reena "Kumar, Rakesh" https://www.zbmath.org/authors/?q=ai:kumar.rakesh.3|kumar.rakesh.4|kumar.rakesh.6|kumar.rakesh.1 "Kumar, Ravinder" https://www.zbmath.org/authors/?q=ai:kumar.ravinder.6|kumar.ravinder.4 "Srivastava, K." https://www.zbmath.org/authors/?q=ai:srivastava.kamal|srivastava.kavita|srivastava.k-d|srivastava.kunal|srivastava.kailash-n|srivastava.kumari-sweta|srivastava.krishna-m|srivastava.kumar-vaibhav|srivastava.k-c|srivastava.kalpana|srivastava.k-b|srivastava.kishor-kumar "Baleanu, D." https://www.zbmath.org/authors/?q=ai:baleanu.dumitru-i Summary: In current analysis, a novel computational approach depending on shifted Lucas polynomials (SLPs) and collocation points is established for fractional integro-differential equations (FIDEs) of Volterra/Fredholm type. A definition for integer order derivative and the lemma for fractional derivative of SLPs are developed. To convert the given equations into algebraic set of equations, zeros of the Lucas polynomial are used as collocation points. Novel theorems for convergence and error analysis are developed to design rigorous mathematical basis for the scheme. Accuracy is proclaimed through comparison with other known methods. Solving two-dimensional fuzzy Fredholm integral equations via sinc collocation method https://www.zbmath.org/1485.65133 2022-06-24T15:10:38.853281Z "Ma, Yanying" https://www.zbmath.org/authors/?q=ai:ma.yanying "Li, Hu" https://www.zbmath.org/authors/?q=ai:li.hu "Zhang, Suping" https://www.zbmath.org/authors/?q=ai:zhang.suping Summary: In this paper, we present a numerical method to solve two-dimensional fuzzy Fredholm integral equations (2D-FFIE) by combing the sinc method with double exponential (DE) transformation. Using this method, the fuzzy Fredholm integral equations are converted into dual fuzzy linear systems. Convergence analysis is performed in terms of the modulus of continuity. Numerical experiments demonstrate the efficiency of the proposed method. Correction to: Numerical solutions for nonlinear Volterra-Fredholm integral equations of the second kind with a phase lag'' https://www.zbmath.org/1485.65134 2022-06-24T15:10:38.853281Z "Mosa, Gamal A." https://www.zbmath.org/authors/?q=ai:mosa.gamal-a "Abdou, Mohamed A." https://www.zbmath.org/authors/?q=ai:abdou.mohamed-aly-mohamed|abdou.mohamed-abdella "Rahby, Ahmed S." https://www.zbmath.org/authors/?q=ai:rahby.ahmed-s Corrects several typos (especially in formulas) in the authors' paper [ibid. 6, No. 8, 8525--8543 (2021; Zbl 1485.65135)]. Numerical solutions for nonlinear Volterra-Fredholm integral equations of the second kind with a phase lag https://www.zbmath.org/1485.65135 2022-06-24T15:10:38.853281Z "Mosa, Gamal A." https://www.zbmath.org/authors/?q=ai:mosa.gamal-a "Abdou, Mohamed A." https://www.zbmath.org/authors/?q=ai:abdou.mohamed-aly-mohamed|abdou.mohamed-abdella "Rahby, Ahmed S." https://www.zbmath.org/authors/?q=ai:rahby.ahmed-s Summary: This study is focused on the numerical solutions of the nonlinear Volterra-Fredholm integral equations (NV-FIEs) of the second kind, which have several applications in physical mathematics and contact problems. Herein, we develop a new technique that combines the modified Adomian decomposition method and the quadrature (trapezoidal and Weddle) rules that used when the definite integral could be extremely difficult, for approximating the solutions of the NV-FIEs of second kind with a phase lag. Foremost, Picard's method and Banach's fixed point theorem are implemented to discuss the existence and uniqueness of the solution. Furthermore, numerical examples are presented to highlight the proposed method's effectiveness, wherein the results are displayed in group of tables and figures to illustrate the applicability of the theoretical results. Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind https://www.zbmath.org/1485.65136 2022-06-24T15:10:38.853281Z "Tynda, Aleksandr Nikolaevich" https://www.zbmath.org/authors/?q=ai:tynda.alexander-n "Noĭyagdam, Samad" https://www.zbmath.org/authors/?q=ai:noeiaghdam.samad "Sidorov, Denis Nikolaevich" https://www.zbmath.org/authors/?q=ai:sidorov.denis-nikolaevich Summary: The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gausstype quadrature formula is used to approximate integrals during the discretization of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to find optimal parameters of the projective method. The numerical examples are included to illustrate the efficiency of proposed novel collocation method. Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels https://www.zbmath.org/1485.65137 2022-06-24T15:10:38.853281Z "Vabishchevich, P. N." https://www.zbmath.org/authors/?q=ai:vabishchevich.petr-n Summary: We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work with an approximate solution for all previous points in time. In this paper, the considered nonlocal problem is transformed into a local one; a loosely coupled equation system with additional ordinary differential equations is solved. This approach is based on the approximation of the difference kernel by the sum of exponentials. Estimates for the stability of the solution concerning the initial data and the right-hand side for the corresponding Cauchy problem are obtained. Two-level schemes with weights with convenient computational implementation are constructed and investigated. The theoretical consideration is supplemented by the results of the numerical solution of the integrodifferential equation when the kernel is the stretching exponential function. Time-consistent evaluation of credit risk with contagion https://www.zbmath.org/1485.91238 2022-06-24T15:10:38.853281Z "Ketelbuters, John-John" https://www.zbmath.org/authors/?q=ai:ketelbuters.john-john "Hainaut, Donatien" https://www.zbmath.org/authors/?q=ai:hainaut.donatien In this paper, the authors present an intensity approach to credit risk. The defaults of companies are modelled by a point process $$(P_t)_{t \geq 0}$$, which is of the form $P_t = \sum_{k=1}^{N_t} \xi_k.$ Here $$(N_t)_{t \geq 0}$$ is a point process with intensity process $$(\lambda_t)_{t \geq 0}$$, and $$\xi_1,\xi_2,\ldots$$ are independent identically distributed random variables. It is assumed that the intensity process $$(\lambda_t)_{t \geq 0}$$ satisfies the stochastic differential equation $\text{d} \lambda_t = \kappa(\theta - \lambda_t) \text{d}t + \eta \text{d}P_t + \sqrt{\lambda_t} \sigma \text{d}W_t,$ where $$(W_t)_{t \geq 0}$$ is a standard Brownian motion, $$\kappa,\theta,\eta > 0$$ and $$\sigma \geq 0$$ are constants, and concerning the initial value it is assumed that $$\lambda_0 \in [\theta,+\infty[$$. The authors derive concrete expression for the expectations $\mathbb{E}[\lambda_t], \quad t \geq 0,$ and for the variances $\mathbb{V}\text{ar}(\lambda_t), \quad t \geq 0.$ Furthermore, they derive expressions for the Laplace transform. Namely, introducing for any $$r \in \mathbb{R}$$ the process $$(P_t^r)_{t \geq 0}$$ as $P_t^r := \int_0^t e^{-rs} \text{d}P_s,$ and introducing the process $$(\Lambda_t)_{t \geq 0}$$ as $\Lambda_t := \int_0^t \lambda_u \text{d}u,$ they show that $\mathbb{E}[\exp \{ -v_1(N_T - N_t) - v_2(P_T^r - P_t^r) - v_2(\Lambda_T - \Lambda_t) \} | \mathcal{F}_t] = \exp \{ A(v,t,T) + \lambda_t B(v,t,T) \}$ for all $$0 \leq t \leq T$$ and $$v \in \mathbb{R}^3$$, where $$A$$ and $$B$$ satisfy a system of ordinary differential equations. The authors also deal with time-consistent evaluations. More precisely, they derive the time-consistent evaluation function derived from the variance principle, from the standard-deviation principle, from the mean value principle, and from the exponential principle. Numerical applications are presented as well. Reviewer: Stefan Tappe (Freiburg) Approximate controllability of noninstantaneous impulsive Hilfer fractional integrodifferential equations with fractional Brownian motion https://www.zbmath.org/1485.93055 2022-06-24T15:10:38.853281Z "Ahmed, Hamdy M." https://www.zbmath.org/authors/?q=ai:ahmed.hamdy-m "El-Borai, Mahmoud M." https://www.zbmath.org/authors/?q=ai:el-borai.mahmoud-m "El Bab, A. S. Okb" https://www.zbmath.org/authors/?q=ai:okb-el-bab.a-s "Ramadan, M. Elsaid" https://www.zbmath.org/authors/?q=ai:ramadan.m-elsaid Summary: We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate set of sufficient conditions is derived for the considered system to be approximately controllable. For the main results, we use fractional calculus, stochastic analysis, fractional power of operators and Sadovskii's fixed point theorem. At the end, an example is also given to show the applicability of our obtained theory. On unified framework for nonlinear grey system models: an integro-differential equation perspective https://www.zbmath.org/1485.93230 2022-06-24T15:10:38.853281Z "Yang, Lu" https://www.zbmath.org/authors/?q=ai:yang.lu "Xie, Naiming" https://www.zbmath.org/authors/?q=ai:xie.naiming "Wei, Baolei" https://www.zbmath.org/authors/?q=ai:wei.baolei "Wang, Xiaolei" https://www.zbmath.org/authors/?q=ai:wang.xiaolei Summary: Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited attention has been paid to the relationship among diverse models and the modelling mechanism. The current paper proposes a unified framework and reconstructs the unified model from an integro-differential equation perspective. First, we propose a methodological framework that subsumes various nonlinear grey system models as special cases, providing a cumulative sum series-orientated modelling paradigm. Then, by introducing an integral operator, the unified model is reduced to an equivalent integro-differential equation; on this basis, the structural parameters and initial value are estimated simultaneously via the integral matching approach. The modelling procedure comparison further indicates that the integral matching-based integro-differential equation provides a direct modelling paradigm. Next, large-scale Monte Carlo simulations are conducted to compare the finite sample performance, and the results show that the reduced model has higher accuracy and robustness to noise. Applications of forecasting the municipal sewage discharge and water consumption in the Yangtze river delta of China further illustrate the effectiveness of the reconstructed nonlinear grey models. Quasilinearization method for an impulsive integro-differential system with delay https://www.zbmath.org/1485.93270 2022-06-24T15:10:38.853281Z "Hu, Bing" https://www.zbmath.org/authors/?q=ai:hu.bing "Wang, Zhizhi" https://www.zbmath.org/authors/?q=ai:wang.zhizhi "Xu, Minbo" https://www.zbmath.org/authors/?q=ai:xu.minbo "Wang, Dingjiang" https://www.zbmath.org/authors/?q=ai:wang.dingjiang Summary: In this paper, we obtain solution sequences converging uniformly and quadratically to extremal solutions of an impulsive integro-differential system with delay. The main tools are the method of quasilinearization and the monotone iterative. The results obtained are more general and applicable than previous studies, especially the quadratic convergence of the solution for a class of integro-differential equations, which have been involved little by now. On uniform asymptotic stability of nonlinear Volterra integro-differential equations https://www.zbmath.org/1485.93471 2022-06-24T15:10:38.853281Z "Pham Huu Anh Ngoc" https://www.zbmath.org/authors/?q=ai:pham-huu-anh-ngoc. "Le Trung Hieu" https://www.zbmath.org/authors/?q=ai:le-trung-hieu. Summary: Using a novel approach, we present some new scalar criteria for the uniform asymptotic stability of general nonlinear Volterra integro-differential equations. Discussion and illustrative examples of the obtained results are given.