# zbMATH — the first resource for mathematics

## Fractional Calculus & Applied Analysis

### An International Journal for Theory and Applications

 Short Title: Fract. Calc. Appl. Anal. Publisher: De Gruyter, Warsaw; Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Sofia ISSN: 1311-0454; 1314-2224/e Online: https://www.degruyter.com/journal/key/fca/htmlhttps://link.springer.com/journal/13540/volumes-and-issueshttp://www.math.bas.bg/~fcaa/ Comments: Indexed cover-to-cover; This journal is available open access.
 Documents Indexed: 1,170 Publications (since 1998) References Indexed: 736 Publications with 22,550 References.
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#### Latest Issues

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#### Authors

 52 Kiryakova, Virginia S. 32 Samko, Stefan Grigorievich 26 Machado, José António Tenreiro 23 Kilbas, Anatoliĭ Aleksandrovich 21 Mainardi, Francesco 20 Chen, Yangquan 18 Luchko, Yuri 17 Gorenflo, Rudolf 16 Trujillo, Juan J. 15 Umarov, Sabir R. 14 Rubin, Boris 13 Băleanu, Dumitru I. 12 Diethelm, Kai 12 Luchko, Yurii F. 11 Atanackovic, Teodor M. 11 Meerschaert, Mark Marvin 11 Podlubny, Igor 10 Kalla, Shyam Lal 10 Pagnini, Gianni 10 Rusev, Petăr Kirilov 9 Ahmad, Bashir 9 Bazhlekova, Emilia G. 9 Dimovski, Ivan Hristov 9 Kokilashvili, Vakhtang Mikhailovich 9 Przeworska-Rolewicz, Danuta 9 Vu Kim Tuan 9 Yamamoto, Masahiro 8 Benchohra, Mouffak 8 Henderson, Johnny Lee 8 Kirane, Mokhtar 8 Li, Changpin 8 Meskhi, Alexander 8 Owa, Shigeyoshi 8 Pilipović, Stevan 8 Tomovski, Živorad 7 Agarwal, Ravi P. 7 Daftardar-Gejji, Varsha 7 Ford, Neville J. 7 Graef, John R. 7 Karapetyants, Alexey N. 7 Liu, Fawang 7 Nogin, Vladimir Aleksandrovich 7 O’Regan, Donal 7 Paneva-Konovska, Jordanka D. 7 Povstenko, Yuriy Z. 6 Boyadjiev, Lyubomir I. 6 Kaczorek, Tadeusz 6 Karapetyants, Nikolai K. 6 Nigmatullin, Raoul R. 6 Petras, Ivo 6 Rafeiro, Humberto 6 Rogosin, Sergei V. 6 Samko, Natasha 6 Srivastava, Hari Mohan 6 Stanković, Bogoljub 6 Sun, Hongguang 6 Tersian, Stepan Agop 6 Zeng, Caibin 5 Abbas, Said 5 Anh, Vo V. 5 Cernea, Aurelian 5 Chen, Wen 5 Dattoli, Giuseppe 5 Garrappa, Roberto 5 Jacob, Niels 5 Karasev, Denis Nikolaevich 5 Kempfle, Siegmar 5 Lanusse, Patrick 5 Matychyn, Ivan I. 5 McBride, Adam C. 5 Mejjaoli, Hatem 5 Ntouyas, Sotiris K. 5 Saxena, Ram Kishore 5 Skórnik, Krystyna A. 5 Vinagre, Blas Manuel 4 Agrawal, Om Prakash 4 Assal, Miloud 4 Choudhary, Sangita 4 Debnath, Lokenath 4 Ding, Xiaoli 4 Ferreira, Rui A. C. 4 Garra, Roberto 4 Giusti, Andrea 4 Herrmann, Richard 4 Hilfer, Rudolf 4 Klimek, Małgorzata 4 Kochubeĭ, Anatoliĭ Naumovych 4 Kolokoltsov, Vassili N. 4 Kong, Lingju 4 Liang, Yingjie 4 Lopes, António M. 4 Malinowska, Agnieszka Barbara 4 Mathai, Arakaparampli Mathai 4 Metzler, Ralf 4 Neugebauer, Jeffrey T. 4 Nieto Roig, Juan Jose 4 Onyshchenko, Viktoriia 4 Rodríguez-López, Rosana 4 Saigo, Megumi 4 Sandev, Trifce ...and 1,252 more Authors
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#### Fields

 507 Real functions (26-XX) 346 Ordinary differential equations (34-XX) 311 Partial differential equations (35-XX) 232 Special functions (33-XX) 146 Operator theory (47-XX) 135 Integral transforms, operational calculus (44-XX) 131 Probability theory and stochastic processes (60-XX) 115 Numerical analysis (65-XX) 112 Integral equations (45-XX) 96 Harmonic analysis on Euclidean spaces (42-XX) 90 Systems theory; control (93-XX) 85 Functional analysis (46-XX) 66 History and biography (01-XX) 64 Functions of a complex variable (30-XX) 37 Mechanics of deformable solids (74-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 27 General and overarching topics; collections (00-XX) 26 Difference and functional equations (39-XX) 22 Measure and integration (28-XX) 22 Potential theory (31-XX) 20 Fluid mechanics (76-XX) 18 Dynamical systems and ergodic theory (37-XX) 18 Approximations and expansions (41-XX) 17 Abstract harmonic analysis (43-XX) 17 Classical thermodynamics, heat transfer (80-XX) 16 Statistical mechanics, structure of matter (82-XX) 14 Global analysis, analysis on manifolds (58-XX) 14 Information and communication theory, circuits (94-XX) 13 Statistics (62-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Biology and other natural sciences (92-XX) 11 Mechanics of particles and systems (70-XX) 10 Number theory (11-XX) 9 Computer science (68-XX) 9 Optics, electromagnetic theory (78-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Geophysics (86-XX) 6 Operations research, mathematical programming (90-XX) 5 Sequences, series, summability (40-XX) 5 Quantum theory (81-XX) 4 Combinatorics (05-XX) 3 Mathematical logic and foundations (03-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 3 Astronomy and astrophysics (85-XX) 2 Topological groups, Lie groups (22-XX) 2 Convex and discrete geometry (52-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX)

#### Citations contained in zbMATH Open

842 Publications have been cited 10,368 times in 6,294 Documents Cited by Year
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
2001
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
2002
Numerical methods for solving the multi-term time-fractional wave-diffusion equation. Zbl 1312.65138
Liu, Fawang; Meerschaert, Mark; McGough, Robert; Zhuang, Pinghui; Liu, Qingxia
2013
Ten equivalent definitions of the fractional Laplace operator. Zbl 1375.47038
Kwaśnicki, Mateusz
2017
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
1998
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
1999
Computation of the Mittag-Leffler function $$E_{\alpha,\beta}(z)$$ and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
2002
Stochastic solutions for fractional Cauchy problems. Zbl 1057.35102
Baeumer, Boris; Meerschaert, Mark M.
2001
Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Zbl 1198.26012
Luchko, Yury
2009
Numerical approximation of a fractional-in-space diffusion equation. I. Zbl 1126.26009
Ilic, M.; Liu, Fawang; Turner, I.; Anh, V.
2005
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
2007
A survey on impulsive fractional differential equations. Zbl 1344.35169
Wang, JinRong; Fečkan, Michal; Zhou, Yong
2016
Some approximations of fractional order operators used in control theory and applications. Zbl 1111.93302
Vinagre, B. M.; Podlubny, I.; Hernández, A.; Feliu, V.
2000
Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives. Zbl 1182.26011
Hilfer, Rudolf; Luchko, Yury; Tomovski, Živorad
2009
Distributed order time fractional diffusion equation. Zbl 1089.60046
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu.
2003
Distributed order differential equations modelling dielectric induction and diffusion. Zbl 1042.34028
Caputo, Michele
2001
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
2015
A finite element method for time fractional partial differential equations. Zbl 1273.65142
Ford, Neville J.; Xiao, Jingyu; Yan, Yubin
2011
Numerical approximation of a fractional-in space diffusion equation. II. With nonhomogeneous boundary conditions. Zbl 1132.35507
Ilic, M.; Liu, F.; Turner, I.; Anh, V.
2006
Spectral approximations to the fractional integral and derivative. Zbl 1276.26016
Li, Changpin; Zeng, Fanhai; Liu, Fawang
2012
A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Zbl 1312.34005
2014
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
2012
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
2000
A Lyapunov-type inequality for a fractional boundary value problem. Zbl 1312.34013
Ferreira, Rui
2013
The fractional Black-Scholes equation. Zbl 1058.91045
Wyss, Walter
2000
Discrete-time fractional-order controllers. Zbl 1111.93307
2001
Existence of solutions to boundary value problem for impulsive fractional differential equations. Zbl 1308.34010
Bonanno, Gabriele; Rodríguez-López, Rosana; Tersian, Stepan
2014
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
2013
Too much regularity may force too much uniqueness. Zbl 1353.35306
Stynes, Martin
2016
Stability of fractional-order systems with rational orders: a survey. Zbl 1182.26017
Petráš, Ivo
2009
The maximal operator on weighted variable Lebesgue spaces. Zbl 1273.42018
Cruz-Uribe, David; Diening, Lars; Hästö, Peter
2011
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
2000
On the oscillation of fractional differential equations. Zbl 1273.34007
Grace, Said R.; Agarwal, Ravi P.; Wong, Patricia J. Y.; Zafer, Ağacık
2012
Fractional calculus for power functions and eigenvalues of the fractional Laplacian. Zbl 1312.35176
Dyda, Bartłlomiej
2012
Maximum principle and its application for the time-fractional diffusion equations. Zbl 1273.35297
Luchko, Yury
2011
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
1999
On the existence of solutions of fractional integro-differential equations. Zbl 1279.45008
Aghajani, Asadollah; Jalilian, Yaghoub; Trujillo, Juan J.
2012
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
1998
Fractional boundary value problems: analysis and numerical methods. Zbl 1273.65098
Ford, Neville J.; Morgado, M. Luísa
2011
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
2007
Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions. Zbl 1321.49007
Debbouche, Amar; Torres, Delfim F. M.
2015
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. Zbl 1312.35184
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
2014
Fractional diffusion on bounded domains. Zbl 06418052
Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
2015
A novel unstructured mesh finite element method for solving the time-space fractional wave equation on a two-dimensional irregular convex domain. Zbl 1364.65162
Fan, Wenping; Liu, Fawang; Jiang, Xiaoyun; Turner, Ian
2017
Strong maximum principle for fractional diffusion equations and an application to an inverse source problem. Zbl 1346.35216
Liu, Yikan; Rundell, William; Yamamoto, Masahiro
2016
Existence results for fractional functional differential inclusions with infinite delay and applications to control theory. Zbl 1149.26010
Benchohra, M.; Henderson, J.; Ntouyas, S. K.; Ouahab, A.
2008
On the generalized Wright function. Zbl 1027.33015
Kilbas, Anatoly A.; Saigo, Megumi; Trujillo, Juan J.
2002
Erdélyi-Kober fractional diffusion. Zbl 1276.26021
Pagnini, Gianni
2012
On explicit stability conditions for a linear fractional difference system. Zbl 1320.39004
Čermák, Jan; Gyori, István; Nechvátal, Ludĕk
2015
New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions. Zbl 1312.65166
Bhrawy, Ali; Alhamed, Yahia; Baleanu, Dumitru; Al-Zahrani, Abdulrahim
2014
Positive solutions for a system of nonlocal fractional boundary value problems. Zbl 1312.34015
Henderson, Johnny; Luca, Rodica
2013
A brief story about the operators of the generalized fractional calculus. Zbl 1153.26003
Kiryakova, Virginia
2008
Subordination principle for fractional evolution equations. Zbl 1041.34046
Bazhlekova, Emilia G.
2000
A probabilistic interpretation of the fractional-order differentiation. Zbl 1035.26010
2003
On a system of fractional differential equations with coupled integral boundary conditions. Zbl 1315.34012
Henderson, Johnny; Luca, Rodica; Tudorache, Alexandru
2015
A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations. Zbl 1343.34006
Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal
2016
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
2012
Hardy inequality in variable exponent Lebesgue spaces. Zbl 1132.26341
Diening, Lars; Samko, Stefan
2007
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications. Zbl 1428.34001
Sun, HongGuang; Chang, Ailian; Zhang, Yong; Chen, Wen
2019
Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions. Zbl 1279.34007
Graef, John R.; Kong, Lingju; Kong, Qingkai; Wang, Min
2012
Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications. Zbl 1381.35225
Liu, Zhenhai; Zeng, Shengda; Bai, Yunru
2016
Multiple solutions to boundary value problem for impulsive fractional differential equations. Zbl 1312.34024
Rodríguez-López, Rosana; Tersian, Stepan
2014
Linear models of dissipation whose $$Q$$ is almost frequency independent. II. (Reprint). Zbl 1210.65130
Caputo, Michele
2008
From fractal robustness to the CRONE control. Zbl 1111.93310
Oustaloup, Alain; Sabatier, Jocelyn; Lanusse, Patrick
1999
Historical survey: the chronicles of fractional calculus. Zbl 1364.26002
Machado, J. A. Tenreiro; Kiryakova, Virginia
2017
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 06604016
Luchko, Yuri; Yamamoto, Masahiro
2016
Nonpolynomial collocation approximation of solutions to fractional differential equations. Zbl 1312.65124
Ford, Neville J.; Morgado, M. Luísa; Rebelo, Magda
2013
Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions. Zbl 1395.34010
Zhang, Xingqiu; Zhong, Qiuyan
2017
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
2014
Monotone iterative method for a class of nonlinear fractional differential equations. Zbl 1273.34021
Wang, Guotao; Baleanu, Dumitru; Zhang, Lihong
2012
Fractional calculus of variations for a combined Caputo derivative. Zbl 1273.49025
Malinowska, Agnieszka B.; Torres, Delfim F. M.
2011
High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. Zbl 1325.65121
Cao, Jianxiong; Li, Changpin; Chen, YangQuan
2015
Fuzzy fractional integral equations under compactness type condition. Zbl 1312.45009
2012
A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures. Zbl 1312.76058
Chen, Wen; Zhang, Jianjun; Zhang, Jinyang
2013
Some pioneers of the applications of fractional calculus. Zbl 1305.26008
Valério, Duarte; Machado, José Tenreiro; Kiryakova, Virginia
2014
On the existence of blow up solutions for a class of fractional differential equations. Zbl 1312.34007
Bai, Zhanbing; Chen, YangQuan; Lian, Hairong; Sun, Sujing
2014
Well-posedness for the nonlinear fractional Schrödinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation. Zbl 1312.35180
Guo, Boling; Huo, Zhaohui
2013
A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels. Zbl 1376.65159
2017
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
2010
High-order algorithms for Riesz derivative and their applications. III. Zbl 1332.65122
Ding, Hengfei; Li, Changpin
2016
Models of dielectric relaxation based on completely monotone functions. Zbl 06663380
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
2016
Caputo-type modification of the Erdélyi-Kober fractional derivatives. Zbl 1152.26304
Luchko, Yury; Trujillo, Juan J.
2007
An efficient parallel algorithm for the numerical solution of fractional differential equations. Zbl 1273.65101
Diethelm, Kai
2011
Solving fractional delay differential equations: a new approach. Zbl 1317.34159
Daftardar-Gejji, Varsha; Sukale, Yogita; Bhalekar, Sachin
2015
On existence and uniqueness of solutions for semilinear fractional wave equations. Zbl 1362.35323
Kian, Yavar; Yamamoto, Masahiro
2017
Some generalized fractional calculus operators and their applications in integral equations. Zbl 1312.26010
Agrawal, Om P.
2012
Existence and uniqueness of solutions for a system of fractional differential equations. Zbl 1396.34003
Zhou, Yong
2009
On $$q$$-analogues of Caputo derivative and Mittag-Leffler function. Zbl 1157.33325
Rajković, Predag M.; Marinković, Sladjana D.; Stanković, Miomir S.
2007
Fractional differential inclusions with fractional separated boundary conditions. Zbl 1279.34003
2012
And I say to myself: “What a fractional world!”. Zbl 1273.37002
2011
Fractional calculus of the generalized Wright function. Zbl 1144.26008
Kilbas, Anatoly A.
2005
Existence and uniqueness of solutions for a fractional boundary value problem on a graph. Zbl 1308.34012
Graef, John R.; Kong, Lingju; Wang, Min
2014
Decay solutions for a class of fractional differential variational inequalities. Zbl 1319.49012
Dinh Ke, Tran; Van Loi, Nguyen; Obukhovskii, Valeri
2015
On the asymptotic stability of linear system of fractional-order difference equations. Zbl 1312.39019
Abu-Saris, Raghib; Al-Mdallal, Qasem
2013
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
2010
Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative. Zbl 1281.34005
2012
Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data. Zbl 1333.65111
Jin, Bangti; Lazarov, Raytcho; Sheen, Dongwoo; Zhou, Zhi
2016
Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Zbl 1338.60199
Sandev, Trifce; Chechkin, Aleksei; Kantz, Holger; Metzler, Ralf
2015
Eigenvalue comparison for fractional boundary value problems with the Caputo derivative. Zbl 1310.34007
Henderson, Johnny; Kosmatov, Nickolai
2014
Inhomogeneous fractional diffusion equations. Zbl 1202.86005
Baeumer, Boris; Kurita, Satoko; Meerschaert, Mark M.
2005
Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations. Zbl 07337090
Kian, Yavar; Yamamoto, Masahiro
2021
An efficient localized collocation solver for anomalous diffusion on surfaces. Zbl 07382483
Tang, Zhuochao; Fu, Zhuojia; Sun, HongGuang; Liu, Xiaoting
2021
Exact stability and instability regions for two-dimensional linear autonomous multi-order systems of fractional-order differential equations. Zbl 07337092
Brandibur, Oana; Kaslik, Eva
2021
Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives. Zbl 07382465
Kassim, Mohammed D.; Tatar, Nasser-eddine
2021
Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications. Zbl 07382467
2021
Sliding methods for the higher order fractional Laplacians. Zbl 07382485
Wu, Leyun
2021
Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives. Zbl 07337087
Bazhlekova, Emilia
2021
Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators. Zbl 1441.34006
Chen, Pengyu; Zhang, Xuping; Li, Yongxiang
2020
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco
2020
A comment on a controversial issue: a generalized fractional derivative cannot have a regular kernel. Zbl 1437.26010
Hanyga, Andrzej
2020
Degenerate Kirchhoff $$(p, q)$$-fractional systems with critical nonlinearities. Zbl 07268199
Fiscella, Alessio; Pucci, Patrizia
2020
Why fractional derivatives with nonsingular kernels should not be used. Zbl 07268195
Diethelm, Kai; Garrappa, Roberto; Giusti, Andrea; Stynes, Martin
2020
On the kinetics of Hadamard-type fractional differential systems. Zbl 07241998
Ma, Li
2020
On a non-local problem for a multi-term fractional diffusion-wave equation. Zbl 1446.35253
Ruzhansky, Michael; Tokmagambetov, Niyaz; Torebek, Berikbol T.
2020
Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives. Zbl 1441.34009
Hanna, Latif A-M.; Al-Kandari, Maryam; Luchko, Yuri
2020
An averaging principle for stochastic differential equations of fractional order $$0 < \alpha < 1$$. Zbl 07268209
Xu, Wenjing; Xu, Wei; Lu, Kai
2020
Attractivity for differential equations of fractional order and $$\psi$$-Hilfer type. Zbl 07268224
Sousa, J. Vanterler da C.; Benchohra, Mouffak; N&rsquo;Guérékata, Gaston M.
2020
$$\alpha$$-fractionally convex functions. Zbl 1450.26003
Singha, Neelam; Nahak, Chandal
2020
Generalized fractional Poisson process and related stochastic dynamics. Zbl 07268197
Michelitsch, Thomas M.; Riascos, Alejandro P.
2020
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 07268213
Luchko, Yuri
2020
On the harmonic extension approach to fractional powers in Banach spaces. Zbl 07268219
Meichsner, Jan; Seifert, Christian
2020
Initial-value / nonlocal Cauchy problems for fractional differential equations involving $$\psi$$-Hilfer multivariable operators. Zbl 07268220
Liang, Jin; Mu, Yunyi; Xiao, Ti-Jun
2020
Time-changed fractional Ornstein-Uhlenbeck process. Zbl 1450.60030
Ascione, Giacomo; Mishura, Yuliya; Pirozzi, Enrica
2020
Fractional problems with critical nonlinearities by a sublinear perturbation. Zbl 1448.35195
Li, Lin; Tersian, Stepan
2020
Well-posedness of the fractional Zener wave equation for heterogeneous viscoelastic materials. Zbl 1439.35544
Oparnica, Ljubica; Süli, Endre
2020
A note on models for anomalous phase-change processes. Zbl 1439.35573
Ceretani, Andrea N.
2020
Stability and resonance analysis of a general non-commensurate elementary fractional-order system. Zbl 1441.93211
Zhang, Shuo; Liu, Lu; Xue, Dingyu; Chen, YangQuan
2020
Space-time fractional stochastic partial differential equations with Lévy noise. Zbl 1460.60066
Meng, Xiangqian; Nane, Erkan
2020
Stability of scalar nonlinear fractional differential equations with linearly dominated delay. Zbl 1441.34084
Tuan, Hoang The; Siegmund, Stefan
2020
Determination of the order of fractional derivative for subdiffusion equations. Zbl 07329879
Ashurov, Ravshan; Umarov, Sabir
2020
The Green function for a class of Caputo fractional differential equations with a convection term. Zbl 07268202
Bai, Zhanbing; Sun, Sujing; Du, Zengji; Chen, YangQuan
2020
Inverse problem for a multi-term fractional differential equation. Zbl 07268203
Ali, Muhammad; Aziz, Sara; Malik, Salman A.
2020
Maximum principles for a class of generalized time-fractional diffusion equations. Zbl 07268204
Zeng, Shengda; Migórski, Stanisław; Nguyen, Van Thien; Bai, Yunru
2020
Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method. Zbl 07268205
Daoues, Adel; Hammami, Amani; Saoudi, Kamel
2020
Erdélyi-Kober fractional integrals and Radon transforms for mutually orthogonal affine planes. Zbl 1462.44003
Rubin, Boris; Wang, Yingzhan
2020
Fractional abstract Cauchy problem on complex interpolation scales. Zbl 07268221
Lopushansky, Andriy; Lopushansky, Oleh; Szpila, Anna
2020
On representation formulas for solutions of linear differential equations with Caputo fractional derivatives. Zbl 07268222
Gomoyunov, Mikhail I.
2020
A class of linear non-homogenous higher order matrix fractional differential equations: analytical solutions and new technique. Zbl 1451.34007
2020
A note on vanishing Morrey $$\rightarrow$$ VMO result for fractional integrals of variable order. Zbl 1453.46023
Rafeiro, Humberto; Samko, Stefan
2020
Fractional integro-differential equations in Wiener spaces. Zbl 1467.45019
Tuan, Vu Kim
2020
Two high-order time discretization schemes for subdiffusion problems with nonsmooth data. Zbl 07329861
Wang, Yanyong; Yan, Yubin; Yang, Yan
2020
Regularity results for nonlocal evolution Venttsel’ problems. Zbl 07329864
Creo, Simone; Lancia, Maria Rosaria; Nazarov, Alexander I.
2020
Multivariate fractional phase-type distributions. Zbl 07329865
2020
Cauchy problem for general time fractional diffusion equation. Zbl 07329871
Sin, Chung-Sik
2020
Multidimensional van der Corput-type estimates involving Mittag-Leffler functions. Zbl 07329880
Ruzhansky, Michael; Torebek, Berikbol T.
2020
Uniqueness for an inverse source problem of determining a space-dependent source in a non-autonomous time-fractional diffusion equation. Zbl 07329882
Slodička, Marian
2020
Nakhushev extremum principle for a class of integro-differential operators. Zbl 07329883
Pskhu, Arsen
2020
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications. Zbl 1428.34001
Sun, HongGuang; Chang, Ailian; Zhang, Yong; Chen, Wen
2019
Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems. Zbl 1426.34012
Gomoyunov, Mikhail I.
2019
A further extension of Mittag-Leffler function. Zbl 1426.33051
Andrić, Maja; Farid, Ghulam; Pečarić, Josip
2019
Fractional impulsive differential equations: exact solutions, integral equations and short memory case. Zbl 1428.34025
Wu, Guo-Cheng; Zeng, De-Qiang; Baleanu, Dumitru
2019
Well-posedness of time-fractional advection-diffusion-reaction equations. Zbl 1439.35542
McLean, William; Mustapha, Kassem; Ali, Raed; Knio, Omar
2019
Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations. Zbl 1423.35402
Kirane, Mokhtar; Torebek, Berikbol T.
2019
The probabilistic point of view on the generalized fractional partial differential equations. Zbl 07115448
Kolokoltsov, Vassili N.
2019
Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions. Zbl 1426.26015
Liang, Yong Shun
2019
Finite element approximations for fractional evolution problems. Zbl 1426.65145
Acosta, Gabriel; Bersetche, Francisco M.; Borthagaray, Juan Pablo
2019
Asymptotically periodic solutions for Caputo type fractional evolution equations. Zbl 1426.34020
Ren, Lulu; Wang, JinRong; Fečkan, Michal
2019
Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions. Zbl 1429.49031
Li, Xiuwen; Li, Yunxiang; Liu, Zhenhai; Li, Jing
2019
Time optimal controls for fractional differential systems with Riemann-Liouville derivatives. Zbl 1425.93137
Lian, TingTing; Fan, ZhenBin; Li, Gang
2019
Some further results of the Laplace transform for variable-order fractional difference equations. Zbl 1439.65223
Baleanu, Dumitru; Wu, Guo-Cheng
2019
Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order $$1 < \alpha < 2$$. Zbl 1441.93038
Shu, Linxin; Shu, Xiao-Bao; Mao, Jianzhong
2019
Regularity of solutions to space-time fractional wave equations: A PDE approach. Zbl 1427.35335
2019
A variational approach for boundary value problems for impulsive fractional differential equations. Zbl 1426.34004
2019
Fractional calculus in economic growth modelling of the group of seven. Zbl 1426.91163
Tejado, Inés; Pérez, Emiliano; Valério, Duarte
2019
The failure of certain fractional calculus operators in two physical models. Zbl 1427.93054
Ortigueira, Manuel D.; Martynyuk, Valeriy; Fedula, Mykola; Machado, J. Tenreiro
2019
Inverse problems for a class of degenerate evolution equations with Riemann - Liouville derivative. Zbl 1423.35440
Fedorov, Vladimir E.; Nazhimov, Roman R.
2019
On Riesz derivative. Zbl 1426.26010
Cai, Min; Li, Changpin
2019
On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces. Zbl 07115454
Zhang, Ye; Hofmann, Bernd
2019
Supercritical fractional Kirchhoff type problems. Zbl 1437.49011
2019
Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network. Zbl 1434.76053
Mehta, Pavan Pranjivan; Pang, Guofei; Song, Fangying; Karniadakis, George Em
2019
Fractional equations via convergence of forms. Zbl 07195223
Capitanelli, Raffaela; D&rsquo;Ovidio, Mirko
2019
About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof. Zbl 07195224
Cresson, Jacky; Szafrańska, Anna
2019
Existence of solutions for nonlinear fractional order $$p$$-Laplacian differential equations via critical point theory. Zbl 07195227
2019
On the fractional diffusion-advection-reaction equation in $$\mathbb{R}$$. Zbl 1442.34012
Ginting, Victor; Li, Yulong
2019
Fractional calculus of variations: a novel way to look at it. Zbl 1439.49045
Ferreira, Rui A. C.
2019
On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053
Mainardi, Francesco; Masina, Enrico
2019
Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations. Zbl 1422.35162
Butko, Yana A.
2019
Finite-time attractivity for semilinear tempered fractional wave equations. Zbl 1423.35401
Ke, Tran Dinh; Quan, Nguyen Nhu
2019
Fractional-order modelling and parameter identification of electrical coils. Zbl 1427.78013
Abuaisha, Tareq; Kertzscher, Jana
2019
The flaw in the conformable calculus: it is conformable because it is not fractional. Zbl 1426.26007
Abdelhakim, Ahmed A.
2019
Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications. Zbl 07192389
Chen, Churong; Bohner, Martin; Jia, Baoguo
2019
Eigenvalues for a combination between local and nonlocal $$p$$-Laplacians. Zbl 1439.35545
Pezzo, Leandro M. Del; Ferreira, Raúl; Rossi, Julio D.
2019
Global solutions to stochastic Volterra equations driven by Lévy noise. Zbl 1436.60064
Hausenblas, Erika; Kovács, Mihály
2019
A note on fractional powers of strongly positive operators and their applications. Zbl 07115434
2019
Semi-fractional diffusion equations. Zbl 1423.35400
Kern, Peter; Lage, Svenja; Meerschaert, Mark M.
2019
On fractional differential inclusions with nonlocal boundary conditions. Zbl 1428.34012
Castaing, Charles; Godet-Thobie, C.; Phung, Phan D.; Truong, Le X.
2019
A system of coupled multi-term fractional differential equations with three-point coupled boundary conditions. Zbl 1428.34006
Ahmad, Bashir; Alghamdi, Najla; Alsaedi, Ahmed; Ntouya, Sotiris K.
2019
Unique continuation principle for the one-dimensional time-fractional diffusion equation. Zbl 1423.35404
Li, Zhiyuan; Yamamoto, Masahiro
2019
Weighted Hölder continuity of Riemann-Liouville fractional integrals – application to regularity of solutions to fractional Cauchy problems with Carathéodory dynamics. Zbl 1428.34009
Bourdin, Loïc
2019
Green’s functions, positive solutions, and a Lyapunov inequality for a Caputo fractional-derivative boundary value problem. Zbl 1426.34017
Meng, Xiangyun; Stynes, Martin
2019
A survey on fractional asymptotic expansion method: a forgotten theory. Zbl 1437.34014
Sayevand, Khosro; Machado, José A. Tenreiro
2019
Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets. Zbl 1443.43009
Samko, Natasha
2019
Weyl integrals on weighted spaces. Zbl 1466.26006
Kleiner, Tillmann; Hilfer, Rudolf
2019
Compactness criteria for fractional integral operators. Zbl 1466.26007
Kokilashvili, Vakhtang; Mastyło, Mieczysław; Meskhi, Alexander
2019
Identification for control of suspended objects in non-Newtonian fluids. Zbl 1434.76018
Birs, Isabela; Muresan, Cristina; Copot, Dana; Nascu, Ioan; Ionescu, Clara
2019
State-of-art survey of fractional order modeling and estimation methods for Lithium-ion batteries. Zbl 1436.78006
Wang, YaNan; Chen, YangQuan; Liao, XiaoZhong
2019
Porous functions. Zbl 1434.74038
Podlubny, Igor
2019
Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: development and application. Zbl 1439.26029
Zhang, Yong; Sun, HongGuang; Zheng, Chunmiao
2019
The vertical slice transform on the unit sphere. Zbl 1445.44003
Rubin, Boris
2019
Exact asymptotic formulas for the heat kernels of space and time-fractional equations. Zbl 1434.60206
Deng, Chang-Song; Schilling, René L.
2019
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#### Cited by 6,212 Authors

 135 Băleanu, Dumitru I. 121 Ahmad, Bashir 94 Liu, Fawang 94 Machado, José António Tenreiro 81 Ntouyas, Sotiris K. 67 Wang, Jinrong 63 Benchohra, Mouffak 60 Agarwal, Ravi P. 58 O’Regan, Donal 56 Nieto Roig, Juan Jose 51 Turner, Ian William 47 Al-saedi, Ahmed Eid Salem 44 Mainardi, Francesco 42 Chen, Yangquan 41 Anh, Vo V. 41 Zhou, Yong 39 Wang, Hong 38 Meerschaert, Mark Marvin 37 Samko, Stefan Grigorievich 32 Tariboon, Jessada 32 Torres, Delfim Fernando Marado 31 Wang, Guotao 30 Abdeljawad, Thabet 30 Kirane, Mokhtar 29 Abbas, Said 29 Atangana, Abdon 28 Li, Changpin 28 Povstenko, Yuriy Z. 28 Sun, Zhizhong 28 Tarasov, Vasily E. 27 Dehghan Takht Fooladi, Mehdi 27 Liu, Lishan 26 Henderson, Johnny Lee 26 Yamamoto, Masahiro 26 Zheng, Xiangcheng 25 Liu, Zhenhai 25 Mejjaoli, Hatem 25 Rubin, Boris 24 Nguyen Huy Tuan 24 Srivastava, Hari Mohan 24 Sun, Hongguang 24 Wu, Yonghong 23 Atanackovic, Teodor M. 23 Daftardar-Gejji, Varsha 23 Luchko, Yuri 22 Abbaszadeh, Mostafa 22 Samet, Bessem 22 Saxena, Ram Kishore 22 Wu, Guocheng 22 Zaky, Mahmoud A. 22 Zhou, Zhi 21 Lopes, António M. 21 Luca, Rodica 21 Nane, Erkan 21 Tomovski, Živorad 21 Trujillo, Juan J. 21 Zhang, Lihong 20 Agarwal, Praveen 20 de Oliveira, Edmundo Capelas 20 Garrappa, Roberto 20 Pagnini, Gianni 20 Stynes, Martin 20 Yan, Yubin 19 Graef, John R. 19 Jin, Bangti 19 Mathai, Arakaparampli Mathai 19 Momani, Shaher M. 19 Suthar, Daya Lal 19 Zeng, Fanhai 18 Ansari, Alireza 18 Bhalekar, Sachin 18 Cui, Yujun 18 Deng, Weihua 18 Fečkan, Michal 18 Jiang, Xiaoyun 18 Khristova, Snezhana G. 18 Leonenko, Nikolai N. 18 Lizama, Carlos 18 Sayevand, Khosro 18 Vanterler da Costa Sousa, José 17 Doungmo Goufo, Emile Franc 17 Feng, Libo 17 Gómez-Aguilar, José Francisco 17 Gorenflo, Rudolf 17 Huang, Chengming 17 Karniadakis, George Em 17 Li, Hong 17 Liu, Yang 17 Odibat, Zaid M. 17 Sandev, Trifce 17 Wei, Ting 17 Yang, Xiao-Jun 17 Zeng, Shengda 16 Bhrawy, Ali Hassan 16 Burrage, Kevin 16 Chen, Wen 16 Gou, Haide 16 Kokilashvili, Vakhtang Mikhailovich 16 Liu, Yuji 16 Torebek, Berikbol Tillabayuly ...and 6,112 more Authors
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#### Cited in 534 Journals

 582 Fractional Calculus & Applied Analysis 279 Advances in Difference Equations 278 Applied Mathematics and Computation 221 Computers & Mathematics with Applications 171 Journal of Computational and Applied Mathematics 125 Communications in Nonlinear Science and Numerical Simulation 118 Nonlinear Dynamics 115 Applied Numerical Mathematics 111 Journal of Mathematical Analysis and Applications 109 Chaos, Solitons and Fractals 102 Abstract and Applied Analysis 95 Journal of Computational Physics 95 Computational and Applied Mathematics 94 Mathematical Problems in Engineering 93 Applied Mathematics Letters 82 Mediterranean Journal of Mathematics 74 Journal of Function Spaces 68 Journal of Scientific Computing 56 Applied Mathematical Modelling 56 Journal of Applied Mathematics and Computing 50 Journal of the Franklin Institute 48 Journal of Mathematical Physics 45 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 44 Numerical Algorithms 44 Discrete Dynamics in Nature and Society 43 Advances in Mathematical Physics 41 Mathematical Methods in the Applied Sciences 39 Nonlinear Analysis. Modelling and Control 39 Boundary Value Problems 39 Fractional Differential Calculus 34 Integral Transforms and Special Functions 33 Inverse Problems 33 Journal of Nonlinear Science and Applications 32 Mathematics and Computers in Simulation 31 Complexity 31 International Journal of Nonlinear Sciences and Numerical Simulation 30 Mathematics 30 International Journal of Applied and Computational Mathematics 29 Journal of Inequalities and Applications 29 Journal of Mathematics 28 Journal of Integral Equations and Applications 28 Chaos 27 SIAM Journal on Scientific Computing 27 Journal of Applied Analysis and Computation 26 Discrete and Continuous Dynamical Systems. Series B 26 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 26 International Journal of Differential Equations 25 Open Mathematics 24 Stochastic Processes and their Applications 24 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 21 Acta Mechanica 21 Applicable Analysis 20 Journal of Functional Analysis 19 Physica A 19 Journal of Differential Equations 19 Discrete and Continuous Dynamical Systems. Series S 19 Tbilisi Mathematical Journal 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 18 Journal of Optimization Theory and Applications 18 SIAM Journal on Numerical Analysis 18 Georgian Mathematical Journal 18 Advances in Computational Mathematics 18 Axioms 17 Journal of Statistical Physics 17 Mathematics of Computation 17 Journal of Mathematical Sciences (New York) 17 Journal of Inverse and Ill-Posed Problems 17 Journal of Vibration and Control 17 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 17 Journal of Pseudo-Differential Operators and Applications 17 Analysis and Mathematical Physics 16 International Journal of Computer Mathematics 16 Mathematical Modelling of Natural Phenomena 15 Computer Methods in Applied Mechanics and Engineering 15 BIT 15 Fuzzy Sets and Systems 15 Proceedings of the American Mathematical Society 15 Fractals 15 Computational Methods in Applied Mathematics 15 Journal of Fixed Point Theory and Applications 15 Afrika Matematika 14 Rocky Mountain Journal of Mathematics 14 Automatica 14 Potential Analysis 14 Lobachevskii Journal of Mathematics 14 Journal of Applied Mathematics 14 Journal of Function Spaces and Applications 14 Complex Analysis and Operator Theory 14 Symmetry 13 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 13 Discrete and Continuous Dynamical Systems 13 Differential Equations and Dynamical Systems 13 International Journal of Applied Mathematics and Computer Science 13 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 13 Inverse Problems in Science and Engineering 13 Advances in Applied Mathematics and Mechanics 12 Ukrainian Mathematical Journal 12 Statistics & Probability Letters 12 Turkish Journal of Mathematics 12 Communications of the Korean Mathematical Society ...and 434 more Journals
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#### Cited in 59 Fields

 2,194 Partial differential equations (35-XX) 2,133 Ordinary differential equations (34-XX) 1,765 Real functions (26-XX) 1,565 Numerical analysis (65-XX) 687 Operator theory (47-XX) 541 Special functions (33-XX) 490 Integral equations (45-XX) 471 Systems theory; control (93-XX) 465 Probability theory and stochastic processes (60-XX) 292 Harmonic analysis on Euclidean spaces (42-XX) 289 Integral transforms, operational calculus (44-XX) 220 Functional analysis (46-XX) 208 Calculus of variations and optimal control; optimization (49-XX) 199 Mechanics of deformable solids (74-XX) 181 Fluid mechanics (76-XX) 169 Biology and other natural sciences (92-XX) 161 Dynamical systems and ergodic theory (37-XX) 157 Difference and functional equations (39-XX) 132 Statistical mechanics, structure of matter (82-XX) 107 Functions of a complex variable (30-XX) 98 Approximations and expansions (41-XX) 85 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 78 Information and communication theory, circuits (94-XX) 72 Classical thermodynamics, heat transfer (80-XX) 71 Statistics (62-XX) 66 Mechanics of particles and systems (70-XX) 62 Global analysis, analysis on manifolds (58-XX) 62 Quantum theory (81-XX) 48 Abstract harmonic analysis (43-XX) 43 Potential theory (31-XX) 40 Computer science (68-XX) 37 Measure and integration (28-XX) 36 Operations research, mathematical programming (90-XX) 34 Linear and multilinear algebra; matrix theory (15-XX) 34 Optics, electromagnetic theory (78-XX) 29 Number theory (11-XX) 24 Geophysics (86-XX) 21 Combinatorics (05-XX) 18 History and biography (01-XX) 16 Sequences, series, summability (40-XX) 16 Differential geometry (53-XX) 14 Topological groups, Lie groups (22-XX) 12 Convex and discrete geometry (52-XX) 9 General topology (54-XX) 8 General and overarching topics; collections (00-XX) 7 Several complex variables and analytic spaces (32-XX) 7 Relativity and gravitational theory (83-XX) 7 Mathematics education (97-XX) 4 Field theory and polynomials (12-XX) 4 Astronomy and astrophysics (85-XX) 3 Group theory and generalizations (20-XX) 3 Geometry (51-XX) 2 Mathematical logic and foundations (03-XX) 2 Algebraic geometry (14-XX) 2 Nonassociative rings and algebras (17-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX)