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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/html
https://link.springer.com/journal/13540/volumes-and-issues
http://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

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 (2019)
21, No. 5 (2019)
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)
6, No. 2 (2003)
6, No. 1 (2003)
5, No. 4 (2002)
5, No. 3 (2002)
5, No. 2 (2002)
5, No. 1 (2002)
4, No. 4 (2001)
4, No. 3 (2001)
4, No. 2 (2001)
4, No. 1 (2001)
3, No. 4 (2000)
3, No. 3 (2000)
...and 9 more Volumes
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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)

Publications by Year

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
326
2001
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
286
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
159
2013
Ten equivalent definitions of the fractional Laplace operator. Zbl 1375.47038
Kwaśnicki, Mateusz
136
2017
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
120
1998
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
106
1999
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
104
2002
Stochastic solutions for fractional Cauchy problems. Zbl 1057.35102
Baeumer, Boris; Meerschaert, Mark M.
97
2001
Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Zbl 1198.26012
Luchko, Yury
94
2009
Numerical approximation of a fractional-in-space diffusion equation. I. Zbl 1126.26009
Ilic, M.; Liu, Fawang; Turner, I.; Anh, V.
90
2005
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
89
2007
A survey on impulsive fractional differential equations. Zbl 1344.35169
Wang, JinRong; Fečkan, Michal; Zhou, Yong
85
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.
83
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
83
2009
Distributed order time fractional diffusion equation. Zbl 1089.60046
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu.
82
2003
Distributed order differential equations modelling dielectric induction and diffusion. Zbl 1042.34028
Caputo, Michele
78
2001
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
78
2015
A finite element method for time fractional partial differential equations. Zbl 1273.65142
Ford, Neville J.; Xiao, Jingyu; Yan, Yubin
75
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.
75
2006
Spectral approximations to the fractional integral and derivative. Zbl 1276.26016
Li, Changpin; Zeng, Fanhai; Liu, Fawang
73
2012
A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Zbl 1312.34005
Ahmad, Bashir; Ntouyas, Sotiris K.
71
2014
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
69
2012
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
65
2000
A Lyapunov-type inequality for a fractional boundary value problem. Zbl 1312.34013
Ferreira, Rui
65
2013
The fractional Black-Scholes equation. Zbl 1058.91045
Wyss, Walter
62
2000
Discrete-time fractional-order controllers. Zbl 1111.93307
Machado, J. A. Tenreiro
60
2001
Existence of solutions to boundary value problem for impulsive fractional differential equations. Zbl 1308.34010
Bonanno, Gabriele; Rodríguez-López, Rosana; Tersian, Stepan
59
2014
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
58
2013
Too much regularity may force too much uniqueness. Zbl 1353.35306
Stynes, Martin
51
2016
Stability of fractional-order systems with rational orders: a survey. Zbl 1182.26017
Petráš, Ivo
48
2009
The maximal operator on weighted variable Lebesgue spaces. Zbl 1273.42018
Cruz-Uribe, David; Diening, Lars; Hästö, Peter
47
2011
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
46
2000
On the oscillation of fractional differential equations. Zbl 1273.34007
Grace, Said R.; Agarwal, Ravi P.; Wong, Patricia J. Y.; Zafer, Ağacık
46
2012
Fractional calculus for power functions and eigenvalues of the fractional Laplacian. Zbl 1312.35176
Dyda, Bartłlomiej
46
2012
Maximum principle and its application for the time-fractional diffusion equations. Zbl 1273.35297
Luchko, Yury
45
2011
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
44
1999
On the existence of solutions of fractional integro-differential equations. Zbl 1279.45008
Aghajani, Asadollah; Jalilian, Yaghoub; Trujillo, Juan J.
44
2012
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
44
1998
Fractional boundary value problems: analysis and numerical methods. Zbl 1273.65098
Ford, Neville J.; Morgado, M. Luísa
43
2011
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
43
2007
Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions. Zbl 1321.49007
Debbouche, Amar; Torres, Delfim F. M.
42
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
42
2014
Fractional diffusion on bounded domains. Zbl 06418052
Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
41
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
41
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
41
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.
41
2008
On the generalized Wright function. Zbl 1027.33015
Kilbas, Anatoly A.; Saigo, Megumi; Trujillo, Juan J.
40
2002
Erdélyi-Kober fractional diffusion. Zbl 1276.26021
Pagnini, Gianni
39
2012
On explicit stability conditions for a linear fractional difference system. Zbl 1320.39004
Čermák, Jan; Gyori, István; Nechvátal, Ludĕk
39
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
39
2014
Positive solutions for a system of nonlocal fractional boundary value problems. Zbl 1312.34015
Henderson, Johnny; Luca, Rodica
39
2013
A brief story about the operators of the generalized fractional calculus. Zbl 1153.26003
Kiryakova, Virginia
39
2008
Subordination principle for fractional evolution equations. Zbl 1041.34046
Bazhlekova, Emilia G.
38
2000
A probabilistic interpretation of the fractional-order differentiation. Zbl 1035.26010
Machado, J. A. Tenreiro
38
2003
On a system of fractional differential equations with coupled integral boundary conditions. Zbl 1315.34012
Henderson, Johnny; Luca, Rodica; Tudorache, Alexandru
38
2015
A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations. Zbl 1343.34006
Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal
38
2016
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
38
2012
Hardy inequality in variable exponent Lebesgue spaces. Zbl 1132.26341
Diening, Lars; Samko, Stefan
38
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
38
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
37
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
37
2016
Multiple solutions to boundary value problem for impulsive fractional differential equations. Zbl 1312.34024
Rodríguez-López, Rosana; Tersian, Stepan
36
2014
Linear models of dissipation whose \(Q\) is almost frequency independent. II. (Reprint). Zbl 1210.65130
Caputo, Michele
36
2008
From fractal robustness to the CRONE control. Zbl 1111.93310
Oustaloup, Alain; Sabatier, Jocelyn; Lanusse, Patrick
35
1999
Historical survey: the chronicles of fractional calculus. Zbl 1364.26002
Machado, J. A. Tenreiro; Kiryakova, Virginia
35
2017
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 06604016
Luchko, Yuri; Yamamoto, Masahiro
35
2016
Nonpolynomial collocation approximation of solutions to fractional differential equations. Zbl 1312.65124
Ford, Neville J.; Morgado, M. Luísa; Rebelo, Magda
35
2013
Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions. Zbl 1395.34010
Zhang, Xingqiu; Zhong, Qiuyan
35
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
34
2014
Monotone iterative method for a class of nonlinear fractional differential equations. Zbl 1273.34021
Wang, Guotao; Baleanu, Dumitru; Zhang, Lihong
34
2012
Fractional calculus of variations for a combined Caputo derivative. Zbl 1273.49025
Malinowska, Agnieszka B.; Torres, Delfim F. M.
34
2011
High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. Zbl 1325.65121
Cao, Jianxiong; Li, Changpin; Chen, YangQuan
34
2015
Fuzzy fractional integral equations under compactness type condition. Zbl 1312.45009
Agarwal, Ravi; Arshad, Sadia; O’Regan, Donal; Lupulescu, Vasile
34
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
34
2013
Some pioneers of the applications of fractional calculus. Zbl 1305.26008
Valério, Duarte; Machado, José Tenreiro; Kiryakova, Virginia
33
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
33
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
33
2013
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
33
2017
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
33
2010
High-order algorithms for Riesz derivative and their applications. III. Zbl 1332.65122
Ding, Hengfei; Li, Changpin
32
2016
Models of dielectric relaxation based on completely monotone functions. Zbl 06663380
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
32
2016
Caputo-type modification of the Erdélyi-Kober fractional derivatives. Zbl 1152.26304
Luchko, Yury; Trujillo, Juan J.
32
2007
An efficient parallel algorithm for the numerical solution of fractional differential equations. Zbl 1273.65101
Diethelm, Kai
31
2011
Solving fractional delay differential equations: a new approach. Zbl 1317.34159
Daftardar-Gejji, Varsha; Sukale, Yogita; Bhalekar, Sachin
31
2015
On existence and uniqueness of solutions for semilinear fractional wave equations. Zbl 1362.35323
Kian, Yavar; Yamamoto, Masahiro
31
2017
Some generalized fractional calculus operators and their applications in integral equations. Zbl 1312.26010
Agrawal, Om P.
31
2012
Existence and uniqueness of solutions for a system of fractional differential equations. Zbl 1396.34003
Zhou, Yong
31
2009
On \(q\)-analogues of Caputo derivative and Mittag-Leffler function. Zbl 1157.33325
Rajković, Predag M.; Marinković, Sladjana D.; Stanković, Miomir S.
31
2007
Fractional differential inclusions with fractional separated boundary conditions. Zbl 1279.34003
Ahmad, Bashir; Ntouyas, Sotiris K.
30
2012
And I say to myself: “What a fractional world!”. Zbl 1273.37002
Tenreiro Machado, J. A.
30
2011
Fractional calculus of the generalized Wright function. Zbl 1144.26008
Kilbas, Anatoly A.
30
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
29
2014
Decay solutions for a class of fractional differential variational inequalities. Zbl 1319.49012
Dinh Ke, Tran; Van Loi, Nguyen; Obukhovskii, Valeri
29
2015
On the asymptotic stability of linear system of fractional-order difference equations. Zbl 1312.39019
Abu-Saris, Raghib; Al-Mdallal, Qasem
29
2013
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
29
2010
Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative. Zbl 1281.34005
Ahmad, Bashir; Nieto, Juan J.
28
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
28
2016
Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Zbl 1338.60199
Sandev, Trifce; Chechkin, Aleksei; Kantz, Holger; Metzler, Ralf
28
2015
Eigenvalue comparison for fractional boundary value problems with the Caputo derivative. Zbl 1310.34007
Henderson, Johnny; Kosmatov, Nickolai
27
2014
Inhomogeneous fractional diffusion equations. Zbl 1202.86005
Baeumer, Boris; Kurita, Satoko; Meerschaert, Mark M.
27
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
3
2021
An efficient localized collocation solver for anomalous diffusion on surfaces. Zbl 07382483
Tang, Zhuochao; Fu, Zhuojia; Sun, HongGuang; Liu, Xiaoting
2
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
2
2021
Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives. Zbl 07382465
Kassim, Mohammed D.; Tatar, Nasser-eddine
1
2021
Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications. Zbl 07382467
Fahad, Hafiz Muhammad; Fernandez, Arran
1
2021
Sliding methods for the higher order fractional Laplacians. Zbl 07382485
Wu, Leyun
1
2021
Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives. Zbl 07337087
Bazhlekova, Emilia
1
2021
Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators. Zbl 1441.34006
Chen, Pengyu; Zhang, Xuping; Li, Yongxiang
21
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
17
2020
A comment on a controversial issue: a generalized fractional derivative cannot have a regular kernel. Zbl 1437.26010
Hanyga, Andrzej
11
2020
Degenerate Kirchhoff \((p, q)\)-fractional systems with critical nonlinearities. Zbl 07268199
Fiscella, Alessio; Pucci, Patrizia
6
2020
Why fractional derivatives with nonsingular kernels should not be used. Zbl 07268195
Diethelm, Kai; Garrappa, Roberto; Giusti, Andrea; Stynes, Martin
5
2020
On the kinetics of Hadamard-type fractional differential systems. Zbl 07241998
Ma, Li
5
2020
On a non-local problem for a multi-term fractional diffusion-wave equation. Zbl 1446.35253
Ruzhansky, Michael; Tokmagambetov, Niyaz; Torebek, Berikbol T.
4
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
4
2020
An averaging principle for stochastic differential equations of fractional order \(0 < \alpha < 1\). Zbl 07268209
Xu, Wenjing; Xu, Wei; Lu, Kai
3
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.
3
2020
\( \alpha \)-fractionally convex functions. Zbl 1450.26003
Singha, Neelam; Nahak, Chandal
3
2020
Generalized fractional Poisson process and related stochastic dynamics. Zbl 07268197
Michelitsch, Thomas M.; Riascos, Alejandro P.
2
2020
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 07268213
Luchko, Yuri
2
2020
On the harmonic extension approach to fractional powers in Banach spaces. Zbl 07268219
Meichsner, Jan; Seifert, Christian
2
2020
Initial-value / nonlocal Cauchy problems for fractional differential equations involving \(\psi\)-Hilfer multivariable operators. Zbl 07268220
Liang, Jin; Mu, Yunyi; Xiao, Ti-Jun
2
2020
Time-changed fractional Ornstein-Uhlenbeck process. Zbl 1450.60030
Ascione, Giacomo; Mishura, Yuliya; Pirozzi, Enrica
2
2020
Fractional problems with critical nonlinearities by a sublinear perturbation. Zbl 1448.35195
Li, Lin; Tersian, Stepan
2
2020
Well-posedness of the fractional Zener wave equation for heterogeneous viscoelastic materials. Zbl 1439.35544
Oparnica, Ljubica; Süli, Endre
2
2020
A note on models for anomalous phase-change processes. Zbl 1439.35573
Ceretani, Andrea N.
2
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
2
2020
Space-time fractional stochastic partial differential equations with Lévy noise. Zbl 1460.60066
Meng, Xiangqian; Nane, Erkan
2
2020
Stability of scalar nonlinear fractional differential equations with linearly dominated delay. Zbl 1441.34084
Tuan, Hoang The; Siegmund, Stefan
2
2020
Determination of the order of fractional derivative for subdiffusion equations. Zbl 07329879
Ashurov, Ravshan; Umarov, Sabir
2
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
1
2020
Inverse problem for a multi-term fractional differential equation. Zbl 07268203
Ali, Muhammad; Aziz, Sara; Malik, Salman A.
1
2020
Maximum principles for a class of generalized time-fractional diffusion equations. Zbl 07268204
Zeng, Shengda; Migórski, Stanisław; Nguyen, Van Thien; Bai, Yunru
1
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
1
2020
Erdélyi-Kober fractional integrals and Radon transforms for mutually orthogonal affine planes. Zbl 1462.44003
Rubin, Boris; Wang, Yingzhan
1
2020
Fractional abstract Cauchy problem on complex interpolation scales. Zbl 07268221
Lopushansky, Andriy; Lopushansky, Oleh; Szpila, Anna
1
2020
On representation formulas for solutions of linear differential equations with Caputo fractional derivatives. Zbl 07268222
Gomoyunov, Mikhail I.
1
2020
A class of linear non-homogenous higher order matrix fractional differential equations: analytical solutions and new technique. Zbl 1451.34007
El-Ajou, Ahmad; Oqielat, Moa&rsquo;ath N.; Al-Zhour, Zeyad; Momani, Shaher
1
2020
A note on vanishing Morrey \(\rightarrow\) VMO result for fractional integrals of variable order. Zbl 1453.46023
Rafeiro, Humberto; Samko, Stefan
1
2020
Fractional integro-differential equations in Wiener spaces. Zbl 1467.45019
Tuan, Vu Kim
1
2020
Two high-order time discretization schemes for subdiffusion problems with nonsmooth data. Zbl 07329861
Wang, Yanyong; Yan, Yubin; Yang, Yan
1
2020
Regularity results for nonlocal evolution Venttsel’ problems. Zbl 07329864
Creo, Simone; Lancia, Maria Rosaria; Nazarov, Alexander I.
1
2020
Multivariate fractional phase-type distributions. Zbl 07329865
Albrecher, Hansjörg; Bladt, Martin; Bladt, Mogens
1
2020
Cauchy problem for general time fractional diffusion equation. Zbl 07329871
Sin, Chung-Sik
1
2020
Multidimensional van der Corput-type estimates involving Mittag-Leffler functions. Zbl 07329880
Ruzhansky, Michael; Torebek, Berikbol T.
1
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
1
2020
Nakhushev extremum principle for a class of integro-differential operators. Zbl 07329883
Pskhu, Arsen
1
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
38
2019
Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems. Zbl 1426.34012
Gomoyunov, Mikhail I.
12
2019
A further extension of Mittag-Leffler function. Zbl 1426.33051
Andrić, Maja; Farid, Ghulam; Pečarić, Josip
12
2019
Fractional impulsive differential equations: exact solutions, integral equations and short memory case. Zbl 1428.34025
Wu, Guo-Cheng; Zeng, De-Qiang; Baleanu, Dumitru
12
2019
Well-posedness of time-fractional advection-diffusion-reaction equations. Zbl 1439.35542
McLean, William; Mustapha, Kassem; Ali, Raed; Knio, Omar
10
2019
Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations. Zbl 1423.35402
Kirane, Mokhtar; Torebek, Berikbol T.
8
2019
The probabilistic point of view on the generalized fractional partial differential equations. Zbl 07115448
Kolokoltsov, Vassili N.
8
2019
Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions. Zbl 1426.26015
Liang, Yong Shun
7
2019
Finite element approximations for fractional evolution problems. Zbl 1426.65145
Acosta, Gabriel; Bersetche, Francisco M.; Borthagaray, Juan Pablo
6
2019
Asymptotically periodic solutions for Caputo type fractional evolution equations. Zbl 1426.34020
Ren, Lulu; Wang, JinRong; Fečkan, Michal
5
2019
Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions. Zbl 1429.49031
Li, Xiuwen; Li, Yunxiang; Liu, Zhenhai; Li, Jing
5
2019
Time optimal controls for fractional differential systems with Riemann-Liouville derivatives. Zbl 1425.93137
Lian, TingTing; Fan, ZhenBin; Li, Gang
5
2019
Some further results of the Laplace transform for variable-order fractional difference equations. Zbl 1439.65223
Baleanu, Dumitru; Wu, Guo-Cheng
4
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
4
2019
Regularity of solutions to space-time fractional wave equations: A PDE approach. Zbl 1427.35335
Otárola, Enrique; Salgado, Abner J.
4
2019
A variational approach for boundary value problems for impulsive fractional differential equations. Zbl 1426.34004
Afrouzi, Ghasem A.; Hadjian, Armin
4
2019
Fractional calculus in economic growth modelling of the group of seven. Zbl 1426.91163
Tejado, Inés; Pérez, Emiliano; Valério, Duarte
4
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
4
2019
Inverse problems for a class of degenerate evolution equations with Riemann - Liouville derivative. Zbl 1423.35440
Fedorov, Vladimir E.; Nazhimov, Roman R.
4
2019
On Riesz derivative. Zbl 1426.26010
Cai, Min; Li, Changpin
4
2019
On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces. Zbl 07115454
Zhang, Ye; Hofmann, Bernd
4
2019
Supercritical fractional Kirchhoff type problems. Zbl 1437.49011
Ambrosio, Vincenzo; Servadei, Raffaella
3
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
3
2019
Fractional equations via convergence of forms. Zbl 07195223
Capitanelli, Raffaela; D&rsquo;Ovidio, Mirko
3
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
3
2019
Existence of solutions for nonlinear fractional order \(p\)-Laplacian differential equations via critical point theory. Zbl 07195227
Nyamoradi, Nemat; Tersian, Stepan
3
2019
On the fractional diffusion-advection-reaction equation in \(\mathbb{R}\). Zbl 1442.34012
Ginting, Victor; Li, Yulong
3
2019
Fractional calculus of variations: a novel way to look at it. Zbl 1439.49045
Ferreira, Rui A. C.
3
2019
On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053
Mainardi, Francesco; Masina, Enrico
3
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.
3
2019
Finite-time attractivity for semilinear tempered fractional wave equations. Zbl 1423.35401
Ke, Tran Dinh; Quan, Nguyen Nhu
3
2019
Fractional-order modelling and parameter identification of electrical coils. Zbl 1427.78013
Abuaisha, Tareq; Kertzscher, Jana
3
2019
The flaw in the conformable calculus: it is conformable because it is not fractional. Zbl 1426.26007
Abdelhakim, Ahmed A.
3
2019
Method of upper and lower solutions for nonlinear Caputo fractional difference equations and its applications. Zbl 07192389
Chen, Churong; Bohner, Martin; Jia, Baoguo
2
2019
Eigenvalues for a combination between local and nonlocal \(p\)-Laplacians. Zbl 1439.35545
Pezzo, Leandro M. Del; Ferreira, Raúl; Rossi, Julio D.
2
2019
Global solutions to stochastic Volterra equations driven by Lévy noise. Zbl 1436.60064
Hausenblas, Erika; Kovács, Mihály
2
2019
A note on fractional powers of strongly positive operators and their applications. Zbl 07115434
Ashyralyev, Allaberen; Hamad, Ayman
2
2019
Semi-fractional diffusion equations. Zbl 1423.35400
Kern, Peter; Lage, Svenja; Meerschaert, Mark M.
2
2019
On fractional differential inclusions with nonlocal boundary conditions. Zbl 1428.34012
Castaing, Charles; Godet-Thobie, C.; Phung, Phan D.; Truong, Le X.
2
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.
2
2019
Unique continuation principle for the one-dimensional time-fractional diffusion equation. Zbl 1423.35404
Li, Zhiyuan; Yamamoto, Masahiro
2
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
2
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
2
2019
A survey on fractional asymptotic expansion method: a forgotten theory. Zbl 1437.34014
Sayevand, Khosro; Machado, José A. Tenreiro
1
2019
Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets. Zbl 1443.43009
Samko, Natasha
1
2019
Weyl integrals on weighted spaces. Zbl 1466.26006
Kleiner, Tillmann; Hilfer, Rudolf
1
2019
Compactness criteria for fractional integral operators. Zbl 1466.26007
Kokilashvili, Vakhtang; Mastyło, Mieczysław; Meskhi, Alexander
1
2019
Identification for control of suspended objects in non-Newtonian fluids. Zbl 1434.76018
Birs, Isabela; Muresan, Cristina; Copot, Dana; Nascu, Ioan; Ionescu, Clara
1
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
1
2019
Porous functions. Zbl 1434.74038
Podlubny, Igor
1
2019
Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: development and application. Zbl 1439.26029
Zhang, Yong; Sun, HongGuang; Zheng, Chunmiao
1
2019
The vertical slice transform on the unit sphere. Zbl 1445.44003
Rubin, Boris
1
2019
Exact asymptotic formulas for the heat kernels of space and time-fractional equations. Zbl 1434.60206
Deng, Chang-Song; Schilling, René L.
1
2019
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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
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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
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50 Journal of the Franklin Institute
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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
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28 Chaos
27 SIAM Journal on Scientific Computing
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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
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19 Physica A
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19 Discrete and Continuous Dynamical Systems. Series S
19 Tbilisi Mathematical Journal
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18 Axioms
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17 Journal of Inverse and Ill-Posed Problems
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17 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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15 Computer Methods in Applied Mechanics and Engineering
15 BIT
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15 Computational Methods in Applied Mathematics
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15 Afrika Matematika
14 Rocky Mountain Journal of Mathematics
14 Automatica
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14 Lobachevskii Journal of Mathematics
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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
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12 Communications of the Korean Mathematical Society
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