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Fractional Calculus & Applied Analysis

An 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-issues
https://www.degruyter.com/journal/key/fca/html
http://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
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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
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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

Citations contained in zbMATH Open

1,065 Publications have been cited 16,673 times in 10,158 Documents Cited by Year
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
404
2001
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
374
2002
Ten equivalent definitions of the fractional Laplace operator. Zbl 1375.47038
Kwaśnicki, Mateusz
270
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
221
2013
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
201
2007
Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives. Zbl 1182.26011
Hilfer, Rudolf; Luchko, Yury; Tomovski, Živorad
173
2009
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
148
1998
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
140
1999
Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Zbl 1198.26012
Luchko, Yury
132
2009
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
131
2002
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
128
2012
A survey on impulsive fractional differential equations. Zbl 1344.35169
Wang, JinRong; Fečkan, Michal; Zhou, Yong
122
2016
Numerical approximation of a fractional-in-space diffusion equation. I. Zbl 1126.26009
Ilic, M.; Liu, Fawang; Turner, I.; Anh, V.
121
2005
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 1499.35642
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
120
2015
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
117
2019
A finite element method for time fractional partial differential equations. Zbl 1273.65142
Ford, Neville J.; Xiao, Jingyu; Yan, Yubin
114
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.
111
2006
Distributed order differential equations modelling dielectric induction and diffusion. Zbl 1042.34028
Caputo, Michele
109
2001
Stochastic solutions for fractional Cauchy problems. Zbl 1057.35102
Baeumer, Boris; Meerschaert, Mark M.
108
2001
Distributed order time fractional diffusion equation. Zbl 1089.60046
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu.
107
2003
A Lyapunov-type inequality for a fractional boundary value problem. Zbl 1312.34013
Ferreira, Rui
103
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.
101
2000
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
Linear models of dissipation whose \(Q\) is almost frequency independent. II. (Reprint). Zbl 1210.65130
Caputo, Michele
97
2008
Spectral approximations to the fractional integral and derivative. Zbl 1276.26016
Li, Changpin; Zeng, Fanhai; Liu, Fawang
94
2012
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
93
2000
The fractional Black-Scholes equation. Zbl 1058.91045
Wyss, Walter
89
2000
Too much regularity may force too much uniqueness. Zbl 1353.35306
Stynes, Martin
88
2016
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
88
2013
The maximal operator on weighted variable Lebesgue spaces. Zbl 1273.42018
Cruz-Uribe, David; Diening, Lars; Hästö, Peter
79
2011
Fractional calculus for power functions and eigenvalues of the fractional Laplacian. Zbl 1312.35176
Dyda, Bartłlomiej
76
2012
Discrete-time fractional-order controllers. Zbl 1111.93307
Machado, J. A. Tenreiro
75
2001
Existence of solutions to boundary value problem for impulsive fractional differential equations. Zbl 1308.34010
Bonanno, Gabriele; Rodríguez-López, Rosana; Tersian, Stepan
75
2014
Some generalized fractional calculus operators and their applications in integral equations. Zbl 1312.26010
Agrawal, Om P.
75
2012
On explicit stability conditions for a linear fractional difference system. Zbl 1320.39004
Čermák, Jan; Gyori, István; Nechvátal, Ludĕk
74
2015
On the oscillation of fractional differential equations. Zbl 1273.34007
Grace, Said R.; Agarwal, Ravi P.; Wong, Patricia J. Y.; Zafer, Ağacık
68
2012
Strong maximum principle for fractional diffusion equations and an application to an inverse source problem. Zbl 1346.35216
Liu, Yikan; Rundell, William; Yamamoto, Masahiro
67
2016
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
66
1999
Stability of fractional-order systems with rational orders: a survey. Zbl 1182.26017
Petráš, Ivo
66
2009
Caputo-type modification of the Erdélyi-Kober fractional derivatives. Zbl 1152.26304
Luchko, Yury; Trujillo, Juan J.
65
2007
On the existence of solutions of fractional integro-differential equations. Zbl 1279.45008
Aghajani, Asadollah; Jalilian, Yaghoub; Trujillo, Juan J.
62
2012
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
61
2012
Fractional diffusion on bounded domains. Zbl 1488.35557
Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
61
2015
On a system of fractional differential equations with coupled integral boundary conditions. Zbl 1315.34012
Henderson, Johnny; Luca, Rodica; Tudorache, Alexandru
61
2015
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
60
1998
On existence and uniqueness of solutions for semilinear fractional wave equations. Zbl 1362.35323
Kian, Yavar; Yamamoto, Masahiro
60
2017
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
60
2007
A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations. Zbl 1343.34006
Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal
60
2016
On the generalized Wright function. Zbl 1027.33015
Kilbas, Anatoly A.; Saigo, Megumi; Trujillo, Juan J.
59
2002
A brief story about the operators of the generalized fractional calculus. Zbl 1153.26003
Kiryakova, Virginia
58
2008
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
Some pioneers of the applications of fractional calculus. Zbl 1305.26008
Valério, Duarte; Machado, José Tenreiro; Kiryakova, Virginia
57
2014
High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. Zbl 1325.65121
Cao, Jianxiong; Li, Changpin; Chen, YangQuan
57
2015
Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions. Zbl 1395.34010
Zhang, Xingqiu; Zhong, Qiuyan
57
2017
Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications. Zbl 1381.35225
Liu, Zhenhai; Zeng, Shengda; Bai, Yunru
57
2016
Erdélyi-Kober fractional diffusion. Zbl 1276.26021
Pagnini, Gianni
56
2012
Maximum principle and its application for the time-fractional diffusion equations. Zbl 1273.35297
Luchko, Yury
56
2011
Initial-boundary value problems for fractional diffusion equations with time-dependent coefficients. Zbl 1398.35271
Kubica, Adam; Yamamoto, Masahiro
56
2018
On \(q\)-analogues of Caputo derivative and Mittag-Leffler function. Zbl 1157.33325
Rajković, Predrag M.; Marinković, Sladjana D.; Stanković, Miomir S.
56
2007
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
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
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
55
2000
Fractional boundary value problems: analysis and numerical methods. Zbl 1273.65098
Ford, Neville J.; Morgado, M. Luísa
55
2011
Subordination principle for fractional evolution equations. Zbl 1041.34046
Bazhlekova, Emilia G.
54
2000
Models of dielectric relaxation based on completely monotone functions. Zbl 1499.78010
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
54
2016
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
Decay solutions for a class of fractional differential variational inequalities. Zbl 1319.49012
Dinh Ke, Tran; Van Loi, Nguyen; Obukhovskii, Valeri
53
2015
On the asymptotic stability of linear system of fractional-order difference equations. Zbl 1312.39019
Abu-Saris, Raghib; Al-Mdallal, Qasem
53
2013
Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions. Zbl 1321.49007
Debbouche, Amar; Torres, Delfim F. M.
52
2015
A probabilistic interpretation of the fractional-order differentiation. Zbl 1035.26010
Machado, J. A. Tenreiro
51
2003
Historical survey: the chronicles of fractional calculus. Zbl 1364.26002
Machado, J. A. Tenreiro; Kiryakova, Virginia
51
2017
Invariant subspace method and exact solutions of certain nonlinear time fractional partial differential equations. Zbl 1499.35682
Sahadevan, Ramajayam; Bakkyaraj, Thangarasu
51
2015
Fuzzy fractional integral equations under compactness type condition. Zbl 1312.45009
Agarwal, Ravi; Arshad, Sadia; O’Regan, Donal; Lupulescu, Vasile
51
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
Solving fractional delay differential equations: a new approach. Zbl 1317.34159
Daftardar-Gejji, Varsha; Sukale, Yogita; Bhalekar, Sachin
50
2015
Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions. Zbl 1368.34017
Yang, Min; Wang, Qiru
49
2017
Fractional calculus in image processing: a review. Zbl 1499.94016
Yang, Qi; Chen, Dali; Zhao, Tiebiao; Chen, YangQuan
49
2016
Nonpolynomial collocation approximation of solutions to fractional differential equations. Zbl 1312.65124
Ford, Neville J.; Morgado, M. Luísa; Rebelo, Magda
49
2013
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco
48
2020
A further extension of Mittag-Leffler function. Zbl 1426.33051
Andrić, Maja; Farid, Ghulam; Pečarić, Josip
48
2018
Hardy inequality in variable exponent Lebesgue spaces. Zbl 1132.26341
Diening, Lars; Samko, Stefan
47
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
47
2017
Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Zbl 1338.60199
Sandev, Trifce; Chechkin, Aleksei; Kantz, Holger; Metzler, Ralf
46
2015
Positive solutions for a system of nonlocal fractional boundary value problems. Zbl 1312.34015
Henderson, Johnny; Luca, Rodica
46
2013
High-order algorithms for Riesz derivative and their applications. III. Zbl 1332.65122
Ding, Hengfei; Li, Changpin
46
2016
Multiple solutions to boundary value problem for impulsive fractional differential equations. Zbl 1312.34024
Rodríguez-López, Rosana; Tersian, Stepan
45
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
45
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
A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures. Zbl 1312.76058
Chen, Wen; Zhang, Jianjun; Zhang, Jinyang
44
2013
Fractional calculus of variations for a combined Caputo derivative. Zbl 1273.49025
Malinowska, Agnieszka B.; Torres, Delfim F. M.
43
2011
And I say to myself: “What a fractional world!”. Zbl 1273.37002
Tenreiro Machado, J. A.
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
Existence and uniqueness of solutions for a system of fractional differential equations. Zbl 1396.34003
Zhou, Yong
42
2009
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
42
2019
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
42
2013
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
Monotone iterative method for a class of nonlinear fractional differential equations. Zbl 1273.34021
Wang, Guotao; Baleanu, Dumitru; Zhang, Lihong
41
2012
An efficient parallel algorithm for the numerical solution of fractional differential equations. Zbl 1273.65101
Diethelm, Kai
41
2011
Variational methods for nonpositive mixed local-nonlocal operators. Zbl 1522.35195
Maione, Alberto; Mugnai, Dimitri; Vecchi, Eugenio
4
2023
A new Bihari inequality and initial value problems of first order fractional differential equations. Zbl 1522.34025
Lan, Kunquan; Webb, J. R. L.
3
2023
Analytical and dimensional properties of fractal interpolation functions on the Sierpiński gasket. Zbl 1522.28011
Verma, Manuj; Priyadarshi, Amit; Verma, Saurabh
3
2023
On the variable order fractional calculus of fractal interpolation functions. Zbl 1522.26008
Valarmathi, R.; Gowrisankar, A.
2
2023
System of fractional boundary value problems at resonance. Zbl 1522.34046
Iatime, Khadidja; Guedda, Lamine; Djebali, Smaïl
2
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
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.
2
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
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
Reconstruction of pointwise sources in a time-fractional diffusion equation. Zbl 1509.35378
Hrizi, Mourad; Hassine, Maatoug; Novotny, Antonio André
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
Exact solutions and Hyers-Ulam stability of fractional equations with double delays. Zbl 1509.34079
Liang, Yixing; Shi, Yang; Fan, Zhenbin
1
2023
Differentiation of integral Mittag-Leffler and integral wright functions with respect to parameters. Zbl 1511.33012
Apelblat, Alexander; González-Santander, Juan Luis
1
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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
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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
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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
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Dual spaces of anisotropic variable Hardy-Lorentz spaces and their applications. Zbl 1511.42023
Liu, Jun; Lu, Yaqian; Huang, Long
1
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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
A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. Zbl 1503.34038
Zhou, Yong; He, Jia Wei
13
2022
Hölder regularity for non-autonomous fractional evolution equations. Zbl 1503.35263
He, Jia Wei; Zhou, Yong
11
2022
Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions. Zbl 1503.26005
Chandra, Subhash; Abbas, Syed
9
2022
Fractional integral operators on Orlicz slice Hardy spaces. Zbl 1503.45013
Ho, Kwok-Pun
9
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
8
2022
Convolution series and the generalized convolution Taylor formula. Zbl 1503.26012
Luchko, Yuri
8
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
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
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
6
2022
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems. Zbl 1503.45015
Zheng, Xiangcheng
6
2022
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition. Zbl 1503.26006
D&rsquo;Elia, Marta; Gulian, Mamikon; Mengesha, Tadele; Scott, James M.
5
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&rsquo;Abbicco, Marcello; Girardi, Giovanni
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
An inverse problem of determining orders of systems of fractional pseudo-differential equations. Zbl 1503.35247
Ashurov, Ravshan; Umarov, Sabir
4
2022
Non-stationary zipper \(\alpha\)-fractal functions and associated fractal operator. Zbl 1503.28010
Jha, Sangita; Verma, Saurabh; Chand, Arya K. B.
4
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
4
2022
Existence and controllability results for Hilfer fractional evolution equations via integral contractors. Zbl 1503.34140
Chaudhary, Renu; Reich, Simeon
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
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
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.
3
2022
Upper and lower estimates for the separation of solutions to fractional differential equations. Zbl 1503.34012
Diethelm, Kai; Tuan, Hoang The
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
Anisotropic variable Campanato-type spaces and their Carleson measure characterizations. Zbl 1503.46024
Huang, Long; Wang, Xiaofeng
2
2022
Dynamical repulsive fractional potential fields in 3D environment. Zbl 1503.70006
Victor, Stéphane; Ruiz, Kendric; Melchior, Pierre; Chaumette, Serge
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
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on \({\mathbb{R}}^d\). Zbl 1503.60080
Chen, Le; Hu, Guannan
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
Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces. Zbl 1503.46022
Karapetyants, Alexey; Morales, Evelyn
2
2022
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems. Zbl 1503.34011
Diethelm, Kai; Thai, Ha Duc; Tuan, Hoang The
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
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
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
Numerical scheme for Erdélyi-Kober fractional diffusion equation using Galerkin-Hermite method. Zbl 1503.65182
Płociniczak, Łukasz; Świtała, Mateusz
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
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
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
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
On the fractional Laplacian of variable order. Zbl 1503.35253
Darve, Eric; D&rsquo;Elia, Marta; Garrappa, Roberto; Giusti, Andrea; Rubio, Natalia L.
1
2022
Fractional boundary value problems. Zbl 1503.60111
D&rsquo;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
Fractional characteristic functions, and a fractional calculus approach for moments of random variables. Zbl 1503.26013
Tomovski, Živorad; Metzler, Ralf; Gerhold, Stefan
1
2022
Vallée-Poussin theorem for fractional functional differential equations. Zbl 1503.34143
Domoshnitsky, Alexander; Padhi, Seshadev; Srivastava, Satyam Narayan
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
Operational calculus for the general fractional derivative and its applications. Zbl 1498.26013
Luchko, Yuri
28
2021
Towards a unified theory of fractional and nonlocal vector calculus. Zbl 1498.26008
D&rsquo;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
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
Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives. Zbl 1499.35618
Bazhlekova, Emilia
15
2021
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106 Machado, José António Tenreiro
89 Benchohra, Mouffak
89 Zhou, Yong
84 Agarwal, Ravi P.
78 O’Regan, Donal
76 Abdeljawad, Thabet
76 Wang, Jinrong
75 Nieto Roig, Juan Jose
64 Turner, Ian William
60 Wang, Hong
51 Chen, Yangquan
50 Samko, Stefan Grigor’evich
49 Zheng, Xiangcheng
48 Anh, Vo V.
48 Mainardi, Francesco
47 Sooppy Nisar, Kottakkaran
46 Abbas, Said
44 Farid, Ghulam
42 Tarasov, Vasily E.
39 Nguyen Huy Tuan
39 Tariboon, Jessada
39 Yamamoto, Masahiro
38 Agarwal, Praveen
38 Kirane, Mokhtar
38 Liu, Lishan
38 Meerschaert, Mark Marvin
38 Torres, Delfim Fernando Marado
37 Li, Changpin
36 Atangana, Abdon
36 Vanterler da Costa Sousa, José
36 Wang, Guotao
36 Zaky, Mahmoud A.
35 Gómez-Aguilar, José Francisco
35 Wu, Guocheng
34 Samet, Bessem
33 Deng, Weihua
33 Sun, Zhizhong
32 Dehghan Takht Fooladi, Mehdi
32 Fernandez, Arran
32 Liu, Yang
32 Srivastava, Hari Mohan
31 de Oliveira, Edmundo Capelas
31 Henderson, Johnny Lee
31 Li, Hong
31 Liu, Zhenhai
31 Mejjaoli, Hatem
31 Wei, Ting
31 Wu, Yonghong
30 Gou, Haide
30 Sun, Hongguang
29 Garrappa, Roberto
29 Povstenko, Yuriy Z.
28 Atanackovic, Teodor M.
28 Jiang, Xiaoyun
28 Karniadakis, George Em
28 Luchko, Yuri
28 Momani, Shaher M.
28 Zeng, Fanhai
27 Alzabut, Jehad O.
27 Doungmo Goufo, Emile Franc
27 Lizama, Carlos
27 Tomovski, Živorad
27 Zhou, Zhi
26 Huang, Chengming
26 Rubin, Boris
26 Sandev, Trifce
26 Shah, Kamal
26 Zeng, Shengda
25 Fečkan, Michal
25 Khristova, Snezhana G.
25 Stynes, Martin Joseph
25 Torebek, Berikbol Tillabayuly
25 Trujillo, Juan J.
25 Yan, Yubin
24 Abbaszadeh, Mostafa
24 Ansari, Alireza
24 Chen, Wen
24 Cui, Yujun
24 Feng, Libo
24 Graef, John R.
24 Lopes, António M.
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23 Daftardar-Gejji, Varsha
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54 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
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33 SIAM Journal on Numerical Analysis
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23 Physics Letters. A
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22 Mathematical Notes
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21 Results in Mathematics
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