Fractional Calculus & Applied AnalysisAn International Journal for Theory and Applications Short Title: Fract. Calc. Appl. Anal. Publisher: Springer Nature Switzerland, Basel; Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Sofia ISSN: 1311-0454; 1314-2224/e Online: https://link.springer.com/journal/13540/volumes-and-issueshttps://www.degruyter.com/journal/key/fca/htmlhttp://www.math.bas.bg/~fcaa/ Comments: Journal; Indexed cover-to-cover Documents Indexed: 1,372 Publications (since 1998) References Indexed: 940 Publications with 29,437 References. all top 5 Latest Issues 26, No. 4 (2023) 26, No. 3 (2023) 26, No. 2 (2023) 26, No. 1 (2023) 25, No. 6 (2022) 25, No. 5 (2022) 25, No. 4 (2022) 25, No. 3 (2022) 25, No. 2 (2022) 25, No. 1 (2022) 24, No. 6 (2021) 24, No. 5 (2021) 24, No. 4 (2021) 24, No. 3 (2021) 24, No. 2 (2021) 24, No. 1 (2021) 23, No. 6 (2020) 23, No. 5 (2020) 23, No. 4 (2020) 23, No. 3 (2020) 23, No. 2 (2020) 23, No. 1 (2020) 22, No. 6 (2019) 22, No. 5 (2019) 22, No. 4 (2019) 22, No. 3 (2019) 22, No. 2 (2019) 22, No. 1 (2019) 21, No. 6 (2018) 21, No. 5 (2018) 21, No. 4 (2018) 21, No. 3 (2018) 21, No. 2 (2018) 21, No. 1 (2018) 20, No. 6 (2017) 20, No. 5 (2017) 20, No. 4 (2017) 20, No. 3 (2017) 20, No. 2 (2017) 20, No. 1 (2017) 19, No. 6 (2016) 19, No. 5 (2016) 19, No. 4 (2016) 19, No. 3 (2016) 19, No. 2 (2016) 19, No. 1 (2016) 18, No. 6 (2015) 18, No. 5 (2015) 18, No. 4 (2015) 18, No. 3 (2015) 18, No. 2 (2015) 18, No. 1 (2015) 17, No. 4 (2014) 17, No. 3 (2014) 17, No. 2 (2014) 17, No. 1 (2014) 16, No. 4 (2013) 16, No. 3 (2013) 16, No. 2 (2013) 16, No. 1 (2013) 15, No. 4 (2012) 15, No. 3 (2012) 15, No. 2 (2012) 15, No. 1 (2012) 14, No. 4 (2011) 14, No. 3 (2011) 14, No. 2 (2011) 14, No. 1 (2011) 13, No. 5 (2010) 13, No. 4 (2010) 13, No. 3 (2010) 13, No. 2 (2010) 13, No. 1 (2010) 12, No. 4 (2009) 12, No. 3 (2009) 12, No. 2 (2009) 12, No. 1 (2009) 11, No. 4 (2008) 11, No. 3 (2008) 11, No. 2 (2008) 11, No. 1 (2008) 10, No. 4 (2007) 10, No. 3 (2007) 10, No. 2 (2007) 10, No. 1 (2007) Index 1-10 (2007) 9, No. 4 (2006) 9, No. 3 (2006) 9, No. 2 (2006) 9, No. 1 (2006) 8, No. 4 (2005) 8, No. 3 (2005) 8, No. 2 (2005) 8, No. 1 (2005) 7, No. 4 (2004) 7, No. 3 (2004) 7, No. 2 (2004) 7, No. 1 (2004) 6, No. 4 (2003) 6, No. 3 (2003) ...and 21 more Volumes all top 5 Authors 53 Kiryakova, Virginia S. 32 Samko, Stefan Grigor’evich 26 Machado, José António Tenreiro 23 Kilbas, Anatoliĭ Aleksandrovich 23 Mainardi, Francesco 22 Chen, Yangquan 19 Luchko, Yuri 17 Gorenflo, Rudolf 16 Trujillo, Juan J. 16 Umarov, Sabir R. 14 Diethelm, Kai 14 Podlubny, Igor 14 Rubin, Boris 13 Băleanu, Dumitru I. 12 Luchko, Yurii F. 11 Atanackovic, Teodor M. 11 Meerschaert, Mark Marvin 10 Kalla, Shyam Lal 10 Pagnini, Gianni 10 Rusev, Petăr Kirilov 10 Vu Kim Tuan 10 Yamamoto, Masahiro 9 Ahmad, Bashir 9 Bazhlekova, Emilia G. 9 Dimovski, Ivan Hristov 9 Kirane, Mokhtar 9 Kokilashvili, Vakhtang 9 Przeworska-Rolewicz, Danuta 9 Tomovski, Živorad 8 Benchohra, Mouffak 8 Henderson, Johnny Lee 8 Karapetyants, Alekseĭ Nikolaevich 8 Li, Changpin 8 Meskhi, Alexander 8 O’Regan, Donal 8 Owa, Shigeyoshi 8 Paneva-Konovska, Jordanka D. 8 Pilipović, Stevan 8 Rogosin, Sergei V. 7 Agarwal, Ravi P. 7 Daftardar-Gejji, Varsha 7 Ford, Neville J. 7 Garrappa, Roberto 7 Graef, John R. 7 Liu, Fawang 7 Nogin, Vladimir Aleksandrovich 7 Petras, Ivo 7 Povstenko, Yuriy Z. 7 Samko, Natasha 7 Sun, Hongguang 7 Zhou, Yong 6 Boyadjiev, Lyubomir I. 6 Chen, Wen 6 Kaczorek, Tadeusz 6 Karapetyants, Nikolaĭ Karapetovich 6 Matychyn, Ivan I. 6 Nieto Roig, Juan Jose 6 Nigmatullin, Raoul R. 6 Rafeiro, Humberto 6 Scalas, Enrico 6 Srivastava, Hari Mohan 6 Stanković, Bogoljub 6 Tersian, Stepan Agop 6 Zeng, Caibin 5 Abbas, Said 5 Anh, Vo V. 5 Ashurov, Ravshan Rajabovich 5 Cernea, Aurelian 5 Dattoli, Giuseppe 5 Ding, Xiaoli 5 Garra, Roberto 5 Giusti, Andrea 5 Hilfer, Rudolf 5 Jacob, Niels 5 Karasev, Denis Nikolaevich 5 Kempfle, Siegmar 5 Kolokoltsov, Vassili N. 5 Lanusse, Patrick 5 Leonenko, Nikolai N. 5 Li, Gang 5 Liang, Yingjie 5 Lopes, António M. 5 Mejjaoli, Hatem 5 Metzler, Ralf 5 Ntouyas, Sotiris K. 5 Onyshchenko, Viktoriia 5 Ortigueira, Manuel D. 5 Saxena, Ram Kishore 5 Skórnik, Krystyna A. 5 Tuan, Hoang The 5 Victor, Stéphane 5 Vinagre, Blas Manuel 5 Virchenko, Nina A. 5 Wu, Guocheng 5 Zayed, Ahmed I. 4 Agrawal, Om Prakash 4 Al-saedi, Ahmed Eid Salem 4 Assal, Miloud 4 Choudhary, Sangita 4 Debnath, Lokenath ...and 1,555 more Authors all top 5 Fields 679 Real functions (26-XX) 403 Ordinary differential equations (34-XX) 395 Partial differential equations (35-XX) 261 Special functions (33-XX) 177 Operator theory (47-XX) 152 Probability theory and stochastic processes (60-XX) 148 Integral transforms, operational calculus (44-XX) 136 Numerical analysis (65-XX) 127 Integral equations (45-XX) 107 Harmonic analysis on Euclidean spaces (42-XX) 106 Systems theory; control (93-XX) 101 Functional analysis (46-XX) 67 Functions of a complex variable (30-XX) 66 History and biography (01-XX) 38 Mechanics of deformable solids (74-XX) 33 Difference and functional equations (39-XX) 32 Calculus of variations and optimal control; optimization (49-XX) 28 Measure and integration (28-XX) 26 General and overarching topics; collections (00-XX) 26 Approximations and expansions (41-XX) 23 Fluid mechanics (76-XX) 22 Potential theory (31-XX) 20 Dynamical systems and ergodic theory (37-XX) 18 Abstract harmonic analysis (43-XX) 18 Information and communication theory, circuits (94-XX) 17 Classical thermodynamics, heat transfer (80-XX) 16 Statistical mechanics, structure of matter (82-XX) 16 Biology and other natural sciences (92-XX) 15 Global analysis, analysis on manifolds (58-XX) 14 Statistics (62-XX) 13 Mechanics of particles and systems (70-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Number theory (11-XX) 11 Optics, electromagnetic theory (78-XX) 10 Computer science (68-XX) 9 Geophysics (86-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 6 Sequences, series, summability (40-XX) 6 Quantum theory (81-XX) 4 Combinatorics (05-XX) 4 Differential geometry (53-XX) 4 Operations research, mathematical programming (90-XX) 3 Mathematical logic and foundations (03-XX) 3 Several complex variables and analytic spaces (32-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) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 1,059 Publications have been cited 16,098 times in 9,807 Documents Cited by ▼ Year ▼ The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156 Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni 383 2001 Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003 Podlubny, Igor 358 2002 Ten equivalent definitions of the fractional Laplace operator. Zbl 1375.47038 Kwaśnicki, Mateusz 259 2017 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 213 2013 Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives. Zbl 1182.26011 Hilfer, Rudolf; Luchko, Yury; Tomovski, Živorad 165 2009 A new dissipation model based on memory mechanism. Zbl 1213.74005 Caputo, M.; Mainardi, F. 145 2007 Random walk models for space-fractional diffusion processes. Zbl 0946.60039 Gorenflo, R.; Mainardi, F. 144 1998 Analytical properties and applications of the Wright function. Zbl 1027.33006 Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 136 1999 Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Zbl 1198.26012 Luchko, Yury 129 2009 Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018 Luchko, Yuri 125 2012 Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016 Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri 125 2002 A survey on impulsive fractional differential equations. Zbl 1344.35169 Wang, JinRong; Fečkan, Michal; Zhou, Yong 119 2016 Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 1499.35642 Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro 118 2015 Numerical approximation of a fractional-in-space diffusion equation. I. Zbl 1126.26009 Ilic, M.; Liu, Fawang; Turner, I.; Anh, V. 117 2005 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 116 2019 A finite element method for time fractional partial differential equations. Zbl 1273.65142 Ford, Neville J.; Xiao, Jingyu; Yan, Yubin 113 2011 Distributed order differential equations modelling dielectric induction and diffusion. Zbl 1042.34028 Caputo, Michele 107 2001 Stochastic solutions for fractional Cauchy problems. Zbl 1057.35102 Baeumer, Boris; Meerschaert, Mark M. 107 2001 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. 106 2006 Distributed order time fractional diffusion equation. Zbl 1089.60046 Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu. 101 2003 A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Zbl 1312.34005 Ahmad, Bashir; Ntouyas, Sotiris K. 101 2014 A Lyapunov-type inequality for a fractional boundary value problem. Zbl 1312.34013 Ferreira, Rui 99 2013 Some approximations of fractional order operators used in control theory and applications. Zbl 1111.93302 Vinagre, B. M.; Podlubny, I.; Hernández, A.; Feliu, V. 98 2000 Spectral approximations to the fractional integral and derivative. Zbl 1276.26016 Li, Changpin; Zeng, Fanhai; Liu, Fawang 90 2012 Linear models of dissipation whose \(Q\) is almost frequency independent. II. (Reprint). Zbl 1210.65130 Caputo, Michele 90 2008 The fractional Black-Scholes equation. Zbl 1058.91045 Wyss, Walter 89 2000 Matrix approach to discrete fractional calculus. Zbl 1030.26011 Podlubny, Igor 88 2000 Too much regularity may force too much uniqueness. Zbl 1353.35306 Stynes, Martin 86 2016 Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179 Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana 85 2013 The maximal operator on weighted variable Lebesgue spaces. Zbl 1273.42018 Cruz-Uribe, David; Diening, Lars; Hästö, Peter 79 2011 Existence of solutions to boundary value problem for impulsive fractional differential equations. Zbl 1308.34010 Bonanno, Gabriele; Rodríguez-López, Rosana; Tersian, Stepan 74 2014 Fractional calculus for power functions and eigenvalues of the fractional Laplacian. Zbl 1312.35176 Dyda, Bartłlomiej 72 2012 Some generalized fractional calculus operators and their applications in integral equations. Zbl 1312.26010 Agrawal, Om P. 72 2012 Discrete-time fractional-order controllers. Zbl 1111.93307 Machado, J. A. Tenreiro 70 2001 On explicit stability conditions for a linear fractional difference system. Zbl 1320.39004 Čermák, Jan; Gyori, István; Nechvátal, Ludĕk 69 2015 On the oscillation of fractional differential equations. Zbl 1273.34007 Grace, Said R.; Agarwal, Ravi P.; Wong, Patricia J. Y.; Zafer, Ağacık 65 2012 Operational method in fractional calculus. Zbl 1030.26009 Luchko, Yuri 64 1999 Strong maximum principle for fractional diffusion equations and an application to an inverse source problem. Zbl 1346.35216 Liu, Yikan; Rundell, William; Yamamoto, Masahiro 63 2016 On the existence of solutions of fractional integro-differential equations. Zbl 1279.45008 Aghajani, Asadollah; Jalilian, Yaghoub; Trujillo, Juan J. 62 2012 Stability of fractional-order systems with rational orders: a survey. Zbl 1182.26017 Petráš, Ivo 62 2009 On a system of fractional differential equations with coupled integral boundary conditions. Zbl 1315.34012 Henderson, Johnny; Luca, Rodica; Tudorache, Alexandru 61 2015 Caputo-type modification of the Erdélyi-Kober fractional derivatives. Zbl 1152.26304 Luchko, Yury; Trujillo, Juan J. 61 2007 On existence and uniqueness of solutions for semilinear fractional wave equations. Zbl 1362.35323 Kian, Yavar; Yamamoto, Masahiro 60 2017 Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001 Luchko, Yu.; Gorenflo, R. 59 1998 Fractional diffusion on bounded domains. Zbl 1488.35557 Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M. 59 2015 A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations. Zbl 1343.34006 Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal 59 2016 An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005 Mainardi, Francesco 58 2012 Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304 Mainardi, Francesco; Gorenflo, Rudolf 58 2007 On the generalized Wright function. Zbl 1027.33015 Kilbas, Anatoly A.; Saigo, Megumi; Trujillo, Juan J. 58 2002 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 57 2017 Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions. Zbl 1395.34010 Zhang, Xingqiu; Zhong, Qiuyan 56 2017 General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 1499.35667 Luchko, Yuri; Yamamoto, Masahiro 56 2016 High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. Zbl 1325.65121 Cao, Jianxiong; Li, Changpin; Chen, YangQuan 56 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 56 2014 Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications. Zbl 1381.35225 Liu, Zhenhai; Zeng, Shengda; Bai, Yunru 56 2016 A brief story about the operators of the generalized fractional calculus. Zbl 1153.26003 Kiryakova, Virginia 56 2008 Maximum principle and its application for the time-fractional diffusion equations. Zbl 1273.35297 Luchko, Yury 55 2011 Fractional boundary value problems: analysis and numerical methods. Zbl 1273.65098 Ford, Neville J.; Morgado, M. Luísa 55 2011 On \(q\)-analogues of Caputo derivative and Mittag-Leffler function. Zbl 1157.33325 Rajković, Predrag M.; Marinković, Sladjana D.; Stanković, Miomir S. 55 2007 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 54 2014 Erdélyi-Kober fractional diffusion. Zbl 1276.26021 Pagnini, Gianni 54 2012 Initial-boundary value problems for fractional diffusion equations with time-dependent coefficients. Zbl 1398.35271 Kubica, Adam; Yamamoto, Masahiro 53 2018 Some pioneers of the applications of fractional calculus. Zbl 1305.26008 Valério, Duarte; Machado, José Tenreiro; Kiryakova, Virginia 53 2014 Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161 Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri 53 2000 Decay solutions for a class of fractional differential variational inequalities. Zbl 1319.49012 Dinh Ke, Tran; Van Loi, Nguyen; Obukhovskii, Valeri 52 2015 Models of dielectric relaxation based on completely monotone functions. Zbl 1499.78010 Garrappa, Roberto; Mainardi, Francesco; Guido, Maione 51 2016 Subordination principle for fractional evolution equations. Zbl 1041.34046 Bazhlekova, Emilia G. 51 2000 Fuzzy fractional integral equations under compactness type condition. Zbl 1312.45009 Agarwal, Ravi; Arshad, Sadia; O’Regan, Donal; Lupulescu, Vasile 50 2012 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 50 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 50 2013 On the asymptotic stability of linear system of fractional-order difference equations. Zbl 1312.39019 Abu-Saris, Raghib; Al-Mdallal, Qasem 50 2013 Solving fractional delay differential equations: a new approach. Zbl 1317.34159 Daftardar-Gejji, Varsha; Sukale, Yogita; Bhalekar, Sachin 50 2015 Historical survey: the chronicles of fractional calculus. Zbl 1364.26002 Machado, J. A. Tenreiro; Kiryakova, Virginia 50 2017 Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions. Zbl 1321.49007 Debbouche, Amar; Torres, Delfim F. M. 49 2015 A probabilistic interpretation of the fractional-order differentiation. Zbl 1035.26010 Machado, J. A. Tenreiro 49 2003 Invariant subspace method and exact solutions of certain nonlinear time fractional partial differential equations. Zbl 1499.35682 Sahadevan, Ramajayam; Bakkyaraj, Thangarasu 48 2015 Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions. Zbl 1368.34017 Yang, Min; Wang, Qiru 48 2017 Nonpolynomial collocation approximation of solutions to fractional differential equations. Zbl 1312.65124 Ford, Neville J.; Morgado, M. Luísa; Rebelo, Magda 47 2013 A further extension of Mittag-Leffler function. Zbl 1426.33051 Andrić, Maja; Farid, Ghulam; Pečarić, Josip 46 2018 A practical guide to Prabhakar fractional calculus. Zbl 1437.33019 Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco 46 2020 Hardy inequality in variable exponent Lebesgue spaces. Zbl 1132.26341 Diening, Lars; Samko, Stefan 46 2007 A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels. Zbl 1376.65159 Parsa Moghaddam, Behrouz; Tenreiro Machado, José António 45 2017 Positive solutions for a system of nonlocal fractional boundary value problems. Zbl 1312.34015 Henderson, Johnny; Luca, Rodica 45 2013 Fractional calculus in image processing: a review. Zbl 1499.94016 Yang, Qi; Chen, Dali; Zhao, Tiebiao; Chen, YangQuan 45 2016 High-order algorithms for Riesz derivative and their applications. III. Zbl 1332.65122 Ding, Hengfei; Li, Changpin 45 2016 Multiple solutions to boundary value problem for impulsive fractional differential equations. Zbl 1312.34024 Rodríguez-López, Rosana; Tersian, Stepan 44 2014 Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006 Al-Refai, Mohammed; Luchko, Yuri 44 2014 Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators. Zbl 1441.34006 Chen, Pengyu; Zhang, Xuping; Li, Yongxiang 44 2020 Fractional calculus of variations for a combined Caputo derivative. Zbl 1273.49025 Malinowska, Agnieszka B.; Torres, Delfim F. M. 43 2011 Fractional impulsive differential equations: exact solutions, integral equations and short memory case. Zbl 1428.34025 Wu, Guo-Cheng; Zeng, De-Qiang; Baleanu, Dumitru 43 2019 Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data. Zbl 1333.65111 Jin, Bangti; Lazarov, Raytcho; Sheen, Dongwoo; Zhou, Zhi 43 2016 A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures. Zbl 1312.76058 Chen, Wen; Zhang, Jianjun; Zhang, Jinyang 42 2013 Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Zbl 1338.60199 Sandev, Trifce; Chechkin, Aleksei; Kantz, Holger; Metzler, Ralf 42 2015 And I say to myself: “What a fractional world!”. Zbl 1273.37002 Tenreiro Machado, J. A. 42 2011 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. 42 2008 Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces. Zbl 1312.47095 Aghajani, Asadollah; Pourhadi, Ehsan; Trujillo, Juan 41 2013 Monotone iterative method for a class of nonlinear fractional differential equations. Zbl 1273.34021 Wang, Guotao; Baleanu, Dumitru; Zhang, Lihong 41 2012 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 41 2012 Fractional differential inclusions with fractional separated boundary conditions. Zbl 1279.34003 Ahmad, Bashir; Ntouyas, Sotiris K. 40 2012 Existence and uniqueness of solutions for a fractional boundary value problem on a graph. Zbl 1308.34012 Graef, John R.; Kong, Lingju; Wang, Min 40 2014 Variational methods for nonpositive mixed local-nonlocal operators. Zbl 1522.35195 Maione, Alberto; Mugnai, Dimitri; Vecchi, Eugenio 4 2023 Subordination and memory dependent kinetics in diffusion and relaxation phenomena. Zbl 1511.45008 Górska, Katarzyna; Horzela, Andrzej 2 2023 Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces. Zbl 1511.35372 Ochoa, Pablo 2 2023 A new Bihari inequality and initial value problems of first order fractional differential equations. Zbl 1522.34025 Lan, Kunquan; Webb, J. R. L. 2 2023 Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket. Zbl 1522.28011 Verma, Manuj; Priyadarshi, Amit; Verma, Saurabh 2 2023 Differentiation of integral Mittag-Leffler and integral wright functions with respect to parameters. Zbl 1511.33012 Apelblat, Alexander; González-Santander, Juan Luis 1 2023 Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities. Zbl 1511.35374 Pham Thanh Tuan; Tran Dinh Ke; Nguyen Nhu Thang 1 2023 Existence and asymptotic behavior of square-mean \(S\)-asymptotically periodic solutions for fractional stochastic evolution equation with delay. Zbl 1511.60097 Li, Qiang; Wu, Xu 1 2023 Subordination principle and approximation of fractional resolvents and applications to fractional evolution equations. Zbl 1511.34084 Zhu, Shouguo; Dai, Peipei; Qu, Yinchun; Li, Gang 1 2023 Dual spaces of anisotropic variable Hardy-Lorentz spaces and their applications. Zbl 1511.42023 Liu, Jun; Lu, Yaqian; Huang, Long 1 2023 Superlinear solutions of sublinear fractional differential equations and regular variation. Zbl 1522.34027 Řehák, Pavel 1 2023 Extremal mild solutions to Hilfer evolution equations with non-instantaneous impulses and nonlocal conditions. Zbl 1522.34086 Gou, Haide; Li, Yongxiang 1 2023 On the variable order fractional calculus of fractal interpolation functions. Zbl 1522.26008 Valarmathi, R.; Gowrisankar, A. 1 2023 Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution. Zbl 1522.65148 Nie, Daxin; Sun, Jing; Deng, Weihua 1 2023 Two families of second-order fractional numerical formulas and applications to fractional differential equations. Zbl 1522.34028 Yin, Baoli; Liu, Yang; Li, Hong; Zhang, Zhimin 1 2023 Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space. Zbl 1522.34023 Haque, Inzamamul; Ali, Javid; Mursaleen, M. 1 2023 Prabhakar function of Le Roy type: a set of results in the complex plane. Zbl 1509.33024 Paneva-Konovska, Jordanka 1 2023 A novel approach to stability analysis of a wide class of irrational linear systems. Zbl 1509.93045 Turkulov, Vukan; Rapaić, Milan R.; Malti, Rachid 1 2023 Qualitative properties of solutions to a nonlinear time-space fractional diffusion equation. Zbl 1509.35338 Borikhanov, Meiirkhan B.; Ruzhansky, Michael; Torebek, Berikbol T. 1 2023 Local and global conserved quantities involving generalized operators. Zbl 1509.70023 Song, Chuan-Jing; Zhang, Yi 1 2023 On the lifting property for the Lipschitz spaces \(\varLambda_{\alpha }\) with \(\alpha >0\). Zbl 1509.33005 Ambrosio, Vincenzo 1 2023 A spectral approach to non-linear weakly singular fractional integro-differential equations. Zbl 1509.45002 Faghih, Amin; Rebelo, Magda 1 2023 A critical elliptic problem involving exponential and singular nonlinearities. Zbl 1509.35341 Choudhuri, Debajyoti; Saoudi, Kamel 1 2023 A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. Zbl 1503.34038 Zhou, Yong; He, Jia Wei 12 2022 Hölder regularity for non-autonomous fractional evolution equations. Zbl 1503.35263 He, Jia Wei; Zhou, Yong 11 2022 Fractional integral operators on Orlicz slice Hardy spaces. Zbl 1503.45013 Ho, Kwok-Pun 9 2022 Convolution series and the generalized convolution Taylor formula. Zbl 1503.26012 Luchko, Yuri 8 2022 Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions. Zbl 1503.26005 Chandra, Subhash; Abbas, Syed 7 2022 Optimal feedback control for a class of fractional evolution equations with history-dependent operators. Zbl 1503.35268 Liu, Yongjian; Liu, Zhenhai; Peng, Sisi; Wen, Ching-Feng 7 2022 Boundedness of fractional integrals on special John-Nirenberg-Campanato and Hardy-type spaces via congruent cubes. Zbl 1503.26009 Jia, Hongchao; Tao, Jin; Yang, Dachun; Yuan, Wen; Zhang, Yangyang 7 2022 The fractional variation and the precise representative of \(BV^{\alpha,p}\) functions. Zbl 1505.46032 Comi, Giovanni E.; Spector, Daniel; Stefani, Giorgio 7 2022 Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition. Zbl 1503.26006 D’Elia, Marta; Gulian, Mamikon; Mengesha, Tadele; Scott, James M. 5 2022 An inverse problem of determining orders of systems of fractional pseudo-differential equations. Zbl 1503.35247 Ashurov, Ravshan; Umarov, Sabir 4 2022 Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders. Zbl 1503.35255 Dien, Nguyen Minh; Nane, Erkan; Minh, Nguyen Dang; Trong, Dang Duc 4 2022 Asymptotic profile for a two-terms time fractional diffusion problem. Zbl 1503.35252 D’Abbicco, Marcello; Girardi, Giovanni 4 2022 Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems. Zbl 1503.45015 Zheng, Xiangcheng 4 2022 Existence and controllability results for Hilfer fractional evolution equations via integral contractors. Zbl 1503.34140 Chaudhary, Renu; Reich, Simeon 4 2022 Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations. Zbl 1503.65194 Zhang, Hui; Zeng, Fanhai; Jiang, Xiaoyun; Karniadakis, George Em 4 2022 Unified predictor-corrector method for fractional differential equations with general kernel functions. Zbl 1503.65146 Wu, Guo-Cheng; Kong, Hua; Luo, Maokang; Fu, Hui; Huang, Lan-Lan 4 2022 Fractional Euler numbers and generalized proportional fractional logistic differential equation. Zbl 1503.34029 Nieto, Juan J. 3 2022 Exterior controllability properties for a fractional Moore-Gibson-Thompson equation. Zbl 1503.35269 Lizama, Carlos; Warma, Mahamadi; Zamorano, Sebastián 3 2022 Non-stationary zipper \(\alpha\)-fractal functions and associated fractal operator. Zbl 1503.28010 Jha, Sangita; Verma, Saurabh; Chand, Arya K. B. 3 2022 Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation. Zbl 1503.35258 Echarghaoui, Rachid; Masmodi, Mohamed 3 2022 Exact solutions of fractional oscillation systems with pure delay. Zbl 1503.34145 Liu, Li; Dong, Qixiang; Li, Gang 3 2022 On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions. Zbl 1503.34141 Diop, Amadou 3 2022 Stochastic solutions of generalized time-fractional evolution equations. Zbl 1503.45005 Bender, Christian; Butko, Yana A. 3 2022 On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition. Zbl 1503.35254 Dien, Nguyen Minh 3 2022 Upper and lower estimates for the separation of solutions to fractional differential equations. Zbl 1503.34012 Diethelm, Kai; Tuan, Hoang The 2 2022 Anisotropic variable Campanato-type spaces and their Carleson measure characterizations. Zbl 1503.46024 Huang, Long; Wang, Xiaofeng 2 2022 Asymptotics of the \(s\)-fractional Gaussian perimeter as \(s\rightarrow 0^+\). Zbl 1503.28004 Carbotti, Alessandro; Cito, Simone; La Manna, Domenico Angelo; Pallara, Diego 2 2022 Numerical conservation laws of time fractional diffusion PDEs. Zbl 1503.65165 Cardone, Angelamaria; Frasca-Caccia, Gianluca 2 2022 On differentiability of solutions of fractional differential equations with respect to initial data. Zbl 1503.34016 Gomoyunov, Mikhail I. 2 2022 A fractional version of the recursive tau method for solving a general class of Abel-Volterra integral equations systems. Zbl 1503.65324 Talaei, Younes; Shahmorad, Sedaghat; Mokhtary, Payam; Faghih, Amin 2 2022 Considerations regarding the accuracy of fractional numerical computations. Zbl 1503.34031 Postavaru, Octavian; Dragoi, Flavius; Toma, Antonela 2 2022 Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations. Zbl 1509.47064 Bender, Christian; Bormann, Marie; Butko, Yana A. 2 2022 Initial-boundary value problems for multi-term time-fractional wave equations. Zbl 1503.35275 Sin, Chung-Sik; Rim, Jin-U; Choe, Hyon-Sok 2 2022 Solvability of infinite systems of fractional differential equations in the double sequence space \(2^c (\triangle)\). Zbl 1503.34026 Mehravaran, Hamid; Kayvanloo, Hojjatollah Amiri; Mursaleen, Mohammad 2 2022 Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain. Zbl 1503.35256 Ding, Xiao-Li; Nieto, Juan J.; Wang, Xiaolong 2 2022 Fractional vector-valued nonuniform MRA and associated wavelet packets on \(L^2\big({\mathbb{R}},{\mathbb{C}}^M\big)\). Zbl 1503.42029 Bhat, M. Younus; Dar, Aamir H. 2 2022 Optimal \(F\)-domain stabilization technique for reduction of commensurate fractional-order SISO systems. Zbl 1503.93016 Mahata, Shibendu; Herencsar, Norbert; Alagoz, Baris Baykant; Yeroglu, Celaleddin 2 2022 On the fractional Laplacian of variable order. Zbl 1503.35253 Darve, Eric; D’Elia, Marta; Garrappa, Roberto; Giusti, Andrea; Rubio, Natalia L. 1 2022 Fractional boundary value problems. Zbl 1503.60111 D’Ovidio, Mirko 1 2022 Stochastic solutions for time-fractional heat equations with complex spatial variables. Zbl 1503.35249 Beghin, Luisa; De Gregorio, Alessandro 1 2022 Sequential generalized Riemann-Liouville derivatives based on distributional convolution. Zbl 1503.26010 Kleiner, Tillmann; Hilfer, Rudolf 1 2022 Monte Carlo method for fractional-order differentiation extended to higher orders. Zbl 1503.65046 Leonenko, Nikolai; Podlubny, Igor 1 2022 Wright functions of the second kind and Whittaker functions. Zbl 1503.33006 Mainardi, Francesco; Paris, Richard B.; Consiglio, Armando 1 2022 The similarity method and explicit solutions for the fractional space one-phase Stefan problems. Zbl 1503.35274 Roscani, Sabrina D.; Tarzia, Domingo A.; Venturato, Lucas D. 1 2022 Fractional characteristic functions, and a fractional calculus approach for moments of random variables. Zbl 1503.26013 Tomovski, Živorad; Metzler, Ralf; Gerhold, Stefan 1 2022 Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems. Zbl 1503.34011 Diethelm, Kai; Thai, Ha Duc; Tuan, Hoang The 1 2022 Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable. Zbl 1503.34037 Zhang, Xingqiu; Shao, Zhuyan; Zhong, Qiuyan 1 2022 Vallée-Poussin theorem for fractional functional differential equations. Zbl 1503.34143 Domoshnitsky, Alexander; Padhi, Seshadev; Srivastava, Satyam Narayan 1 2022 Numerical scheme for Erdélyi-Kober fractional diffusion equation using Galerkin-Hermite method. Zbl 1503.65182 Płociniczak, Łukasz; Świtała, Mateusz 1 2022 Multi-term fractional oscillation integro-differential equations. Zbl 1503.45006 Phung, Tran Dinh; Duc, Dinh Thanh; Tuan, Vu Kim 1 2022 Partially explicit time discretization for time fractional diffusion equation. Zbl 1503.65207 Hu, Jiuhua; Alikhanov, Anatoly; Efendiev, Yalchin; Leung, Wing Tat 1 2022 Discrete fractional distributed Halanay inequality and applications in discrete fractional order neural network systems. Zbl 1503.26035 Liu, Xiang; Yu, Yongguang 1 2022 Existence of an infinite system of fractional hybrid differential equations in a tempered sequence space. Zbl 1509.47110 Das, Anupam; Hazarika, Bipan; Deuri, Bhuban Chandra 1 2022 On solvability for a class of nonlinear systems of differential equations with the Caputo fractional derivative. Zbl 1503.34022 Jolić, Maja; Konjik, Sanja; Mitrović, Darko 1 2022 A non-local semilinear eigenvalue problem. Zbl 1503.35120 Franzina, Giovanni; Licheri, Danilo 1 2022 Caputo delta weakly fractional difference equations. Zbl 1503.39004 Fečkan, Michal; Pospíšil, Michal; Danca, Marius-F.; Wang, JinRong 1 2022 Cauchy problem for non-autonomous fractional evolution equations. Zbl 1509.47065 He, Jia Wei; Zhou, Yong 1 2022 Sensitivity analysis for a fractional stochastic differential equation with \(S^p\)-weighted pseudo almost periodic coefficients and infinite delay. Zbl 1503.34035 Yan, Zuomao 1 2022 Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay. Zbl 1503.34021 He, Bin-Bin; Zhou, Hua-Cheng; Kou, Chun-Hai 1 2022 Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents. Zbl 1503.35281 Zuo, Jiabin; Choudhuri, Debajyoti; Repovš, Dušan D. 1 2022 Dynamical repulsive fractional potential fields in 3D environment. Zbl 1503.70006 Victor, Stéphane; Ruiz, Kendric; Melchior, Pierre; Chaumette, Serge 1 2022 Monte Carlo method for fractional-order differentiation. Zbl 1503.65047 Leonenko, Nikolai; Podlubny, Igor 1 2022 The fractional-order Lorenz-type systems: a review. Zbl 1503.34030 Petráš, Ivo 1 2022 Computation of the inverse Mittag-Leffler function and its application to modeling ultraslow dynamics. Zbl 1503.33017 Liang, Yingjie; Yu, Yue; Magin, Richard L. 1 2022 Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on \({\mathbb{R}}^d\). Zbl 1503.60080 Chen, Le; Hu, Guannan 1 2022 Asymptotics of the Mittag-Leffler function \(E_a(z)\) on the negative real axis when \(a \rightarrow 1\). Zbl 1503.30092 Paris, Richard 1 2022 Mixed stochastic heat equation with fractional Laplacian and gradient perturbation. Zbl 1503.60086 Zili, Mounir; Zougar, Eya 1 2022 Operational calculus for the general fractional derivative and its applications. Zbl 1498.26013 Luchko, Yuri 26 2021 Towards a unified theory of fractional and nonlocal vector calculus. Zbl 1498.26008 D’Elia, Marta; Gulian, Mamikon; Olson, Hayley; Karniadakis, George Em 20 2021 An efficient localized collocation solver for anomalous diffusion on surfaces. Zbl 1498.65176 Tang, Zhuochao; Fu, Zhuojia; Sun, HongGuang; Liu, Xiaoting 17 2021 Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations. Zbl 1474.35657 Kian, Yavar; Yamamoto, Masahiro 16 2021 Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives. Zbl 1499.35618 Bazhlekova, Emilia 15 2021 An inverse problem approach to determine possible memory length of fractional differential equations. Zbl 1498.34028 Gu, Chuan-Yun; Wu, Guo-Cheng; Shiri, Babak 15 2021 Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications. Zbl 1498.26010 Fahad, Hafiz Muhammad; Fernandez, Arran 13 2021 Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas. Zbl 1498.35570 del Teso, Félix; Gómez-Castro, David; Vázquez, Juan Luis 9 2021 Exact stability and instability regions for two-dimensional linear autonomous multi-order systems of fractional-order differential equations. Zbl 1488.34319 Brandibur, Oana; Kaslik, Eva 8 2021 Characterizations of variable martingale Hardy spaces via maximal functions. Zbl 1498.60161 Weisz, Ferenc 8 2021 ...and 959 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 9,520 Authors 188 Băleanu, Dumitru I. 166 Ahmad, Bashir 115 Liu, Fawang 114 Al-saedi, Ahmed Eid Salem 113 Ntouyas, Sotiris K. 99 Machado, José António Tenreiro 89 Benchohra, Mouffak 89 Zhou, Yong 83 Agarwal, Ravi P. 78 O’Regan, Donal 75 Abdeljawad, Thabet 75 Wang, Jinrong 72 Nieto Roig, Juan Jose 61 Turner, Ian William 60 Wang, Hong 50 Chen, Yangquan 50 Samko, Stefan Grigor’evich 47 Anh, Vo V. 47 Mainardi, Francesco 47 Sooppy Nisar, Kottakkaran 46 Abbas, Said 46 Zheng, Xiangcheng 42 Farid, Ghulam 39 Tariboon, Jessada 38 Liu, Lishan 38 Meerschaert, Mark Marvin 38 Nguyen Huy Tuan 38 Torres, Delfim Fernando Marado 38 Yamamoto, Masahiro 37 Agarwal, Praveen 37 Kirane, Mokhtar 36 Wang, Guotao 35 Atangana, Abdon 35 Li, Changpin 35 Tarasov, Vasily E. 35 Vanterler da Costa Sousa, José 35 Zaky, Mahmoud A. 34 Samet, Bessem 32 Dehghan Takht Fooladi, Mehdi 32 Deng, Weihua 32 Liu, Yang 32 Sun, Zhizhong 31 Gómez-Aguilar, José Francisco 31 Henderson, Johnny Lee 31 Li, Hong 31 Liu, Zhenhai 31 Srivastava, Hari Mohan 31 Wu, Guocheng 31 Wu, Yonghong 30 de Oliveira, Edmundo Capelas 30 Fernandez, Arran 30 Gou, Haide 30 Mejjaoli, Hatem 30 Sun, Hongguang 30 Wei, Ting 29 Povstenko, Yuriy Z. 28 Luchko, Yuri 27 Alzabut, Jehad O. 27 Atanackovic, Teodor M. 27 Doungmo Goufo, Emile Franc 27 Karniadakis, George Em 27 Lizama, Carlos 27 Zhou, Zhi 26 Huang, Chengming 26 Momani, Shaher M. 26 Rubin, Boris 26 Tomovski, Živorad 26 Zeng, Fanhai 25 Garrappa, Roberto 25 Khristova, Snezhana G. 25 Shah, Kamal 25 Stynes, Martin Joseph 25 Torebek, Berikbol Tillabayuly 25 Trujillo, Juan J. 25 Yan, Yubin 24 Abbaszadeh, Mostafa 24 Cui, Yujun 24 Fečkan, Michal 24 Feng, Libo 24 Graef, John R. 24 Jiang, Xiaoyun 24 Luca, Rodica 24 Nane, Erkan 24 Ordokhani, Yadollah 24 Razzaghi, Mohsen 24 Sandev, Trifce 24 Zeng, Shengda 24 Zhang, Lihong 23 Daftardar-Gejji, Varsha 23 Hendy, Ahmed S. 23 Jarad, Fahd 23 Li, Yongxiang 23 Lopes, António M. 22 Abdo, Mohammed Salem 22 Ansari, Alireza 22 Chen, Wen 22 Jin, Bangti 22 Jleli, Mohamed Boussairi 22 Ouannas, Adel 22 Pagnini, Gianni ...and 9,420 more Authors all top 5 Cited in 650 Journals 769 Fractional Calculus & Applied Analysis 446 Advances in Difference Equations 310 Applied Mathematics and Computation 269 Computers & Mathematics with Applications 236 Chaos, Solitons and Fractals 216 Journal of Computational and Applied Mathematics 196 Communications in Nonlinear Science and Numerical Simulation 181 Mathematical Methods in the Applied Sciences 140 Computational and Applied Mathematics 134 Applied Numerical Mathematics 133 Nonlinear Dynamics 128 Journal of Mathematical Analysis and Applications 117 Applied Mathematics Letters 114 Journal of Computational Physics 112 Fractals 110 Journal of Function Spaces 107 Boundary Value Problems 104 AIMS Mathematics 102 Mathematical Problems in Engineering 102 Abstract and Applied Analysis 99 Mediterranean Journal of Mathematics 96 Journal of Scientific Computing 84 Journal of Inequalities and Applications 75 Numerical Algorithms 74 Physica A 73 International Journal of Computer Mathematics 69 Applied Mathematical Modelling 69 Journal of Applied Mathematics and Computing 69 International Journal of Applied and Computational Mathematics 66 Mathematics and Computers in Simulation 62 Fractional Differential Calculus 61 Journal of the Franklin Institute 61 Numerical Methods for Partial Differential Equations 58 International Journal of Nonlinear Sciences and Numerical Simulation 55 Nonlinear Analysis. 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