## Fractional Calculus & Applied Analysis

### An International Journal for Theory and Applications

 Short Title: Fract. Calc. Appl. Anal. Publisher: De Gruyter, Warsaw; Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Sofia ISSN: 1311-0454; 1314-2224/e Online: https://www.degruyter.com/journal/key/fca/htmlhttps://link.springer.com/journal/13540/volumes-and-issueshttp://www.math.bas.bg/~fcaa/ Comments: Indexed cover-to-cover; This journal is available open access.
 Documents Indexed: 1,197 Publications (since 1998) References Indexed: 765 Publications with 23,523 References.
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### Latest Issues

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### Authors

 54 Kiryakova, Virginia S. 32 Samko, Stefan Grigorievich 27 Machado, José António Tenreiro 23 Kilbas, Anatoliĭ Aleksandrovich 21 Chen, Yangquan 21 Mainardi, Francesco 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. 12 Podlubny, Igor 11 Atanackovic, Teodor M. 11 Meerschaert, Mark Marvin 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 O’Regan, Donal 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 Paneva-Konovska, Jordanka D. 7 Povstenko, Yuriy Z. 7 Rogosin, Sergei V. 7 Samko, Natasha 6 Boyadjiev, Lyubomir I. 6 Kaczorek, Tadeusz 6 Karapetyants, Nikolai K. 6 Nigmatullin, Raoul R. 6 Petras, Ivo 6 Rafeiro, Humberto 6 Srivastava, Hari Mohan 6 Stanković, Bogoljub 6 Sun, Hongguang 6 Tersian, Stepan Agop 6 Vinagre, Blas Manuel 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 Lopes, António M. 5 Matychyn, Ivan I. 5 McBride, Adam C. 5 Mejjaoli, Hatem 5 Ntouyas, Sotiris K. 5 Ortigueira, Manuel D. 5 Saxena, Ram Kishore 5 Skórnik, Krystyna A. 4 Agrawal, Om Prakash 4 Al-saedi, Ahmed Eid Salem 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 Malinowska, Agnieszka Barbara 4 Mathai, Arakaparampli Mathai 4 Metzler, Ralf 4 Neugebauer, Jeffrey Thomas 4 Nieto Roig, Juan Jose 4 Onyshchenko, Viktoriia 4 Rodríguez-López, Rosana ...and 1,294 more Authors
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### Fields

 526 Real functions (26-XX) 356 Ordinary differential equations (34-XX) 320 Partial differential equations (35-XX) 236 Special functions (33-XX) 153 Operator theory (47-XX) 134 Integral transforms, operational calculus (44-XX) 131 Probability theory and stochastic processes (60-XX) 118 Numerical analysis (65-XX) 113 Integral equations (45-XX) 97 Harmonic analysis on Euclidean spaces (42-XX) 94 Systems theory; control (93-XX) 87 Functional analysis (46-XX) 67 History and biography (01-XX) 64 Functions of a complex variable (30-XX) 38 Mechanics of deformable solids (74-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 27 General and overarching topics; collections (00-XX) 27 Difference and functional equations (39-XX) 23 Measure and integration (28-XX) 22 Potential theory (31-XX) 20 Fluid mechanics (76-XX) 19 Dynamical systems and ergodic theory (37-XX) 19 Approximations and expansions (41-XX) 18 Classical thermodynamics, heat transfer (80-XX) 17 Abstract harmonic analysis (43-XX) 16 Statistical mechanics, structure of matter (82-XX) 15 Global analysis, analysis on manifolds (58-XX) 15 Biology and other natural sciences (92-XX) 15 Information and communication theory, circuits (94-XX) 13 Statistics (62-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Mechanics of particles and systems (70-XX) 10 Number theory (11-XX) 10 Computer science (68-XX) 10 Optics, electromagnetic theory (78-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 8 Geophysics (86-XX) 7 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)

### Citations contained in zbMATH Open

912 Publications have been cited 12,517 times in 7,772 Documents Cited by Year
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
2001
Geometric and physical interpretation of fractional integration and fractional differentiation. Zbl 1042.26003
Podlubny, Igor
2002
Numerical methods for solving the multi-term time-fractional wave-diffusion equation. Zbl 1312.65138
Liu, Fawang; Meerschaert, Mark; McGough, Robert; Zhuang, Pinghui; Liu, Qingxia
2013
Ten equivalent definitions of the fractional Laplace operator. Zbl 1375.47038
Kwaśnicki, Mateusz
2017
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
1998
Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives. Zbl 1182.26011
Hilfer, Rudolf; Luchko, Yury; Tomovski, Živorad
2009
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
1999
Computation of the Mittag-Leffler function $$E_{\alpha,\beta}(z)$$ and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
2002
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
2007
A survey on impulsive fractional differential equations. Zbl 1344.35169
Wang, JinRong; Fečkan, Michal; Zhou, Yong
2016
Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Zbl 1198.26012
Luchko, Yury
2009
Stochastic solutions for fractional Cauchy problems. Zbl 1057.35102
Baeumer, Boris; Meerschaert, Mark M.
2001
Numerical approximation of a fractional-in-space diffusion equation. I. Zbl 1126.26009
Ilic, M.; Liu, Fawang; Turner, I.; Anh, V.
2005
Distributed order differential equations modelling dielectric induction and diffusion. Zbl 1042.34028
Caputo, Michele
2001
A finite element method for time fractional partial differential equations. Zbl 1273.65142
Ford, Neville J.; Xiao, Jingyu; Yan, Yubin
2011
Distributed order time fractional diffusion equation. Zbl 1089.60046
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu.
2003
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
2015
Numerical approximation of a fractional-in space diffusion equation. II. With nonhomogeneous boundary conditions. Zbl 1132.35507
Ilic, M.; Liu, F.; Turner, I.; Anh, V.
2006
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
2012
A Lyapunov-type inequality for a fractional boundary value problem. Zbl 1312.34013
Ferreira, Rui
2013
A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Zbl 1312.34005
2014
Some approximations of fractional order operators used in control theory and applications. Zbl 1111.93302
Vinagre, B. M.; Podlubny, I.; Hernández, A.; Feliu, V.
2000
Spectral approximations to the fractional integral and derivative. Zbl 1276.26016
Li, Changpin; Zeng, Fanhai; Liu, Fawang
2012
The fractional Black-Scholes equation. Zbl 1058.91045
Wyss, Walter
2000
Matrix approach to discrete fractional calculus. Zbl 1030.26011
Podlubny, Igor
2000
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
2013
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications. Zbl 1428.34001
Sun, HongGuang; Chang, Ailian; Zhang, Yong; Chen, Wen
2019
Discrete-time fractional-order controllers. Zbl 1111.93307
2001
Existence of solutions to boundary value problem for impulsive fractional differential equations. Zbl 1308.34010
Bonanno, Gabriele; Rodríguez-López, Rosana; Tersian, Stepan
2014
The maximal operator on weighted variable Lebesgue spaces. Zbl 1273.42018
Cruz-Uribe, David; Diening, Lars; Hästö, Peter
2011
Too much regularity may force too much uniqueness. Zbl 1353.35306
Stynes, Martin
2016
On the oscillation of fractional differential equations. Zbl 1273.34007
Grace, Said R.; Agarwal, Ravi P.; Wong, Patricia J. Y.; Zafer, Ağacık
2012
Fractional calculus for power functions and eigenvalues of the fractional Laplacian. Zbl 1312.35176
Dyda, Bartłlomiej
2012
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
1998
Stability of fractional-order systems with rational orders: a survey. Zbl 1182.26017
Petráš, Ivo
2009
On a system of fractional differential equations with coupled integral boundary conditions. Zbl 1315.34012
Henderson, Johnny; Luca, Rodica; Tudorache, Alexandru
2015
On explicit stability conditions for a linear fractional difference system. Zbl 1320.39004
Čermák, Jan; Gyori, István; Nechvátal, Ludĕk
2015
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
2000
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
1999
Some generalized fractional calculus operators and their applications in integral equations. Zbl 1312.26010
Agrawal, Om P.
2012
On the existence of solutions of fractional integro-differential equations. Zbl 1279.45008
Aghajani, Asadollah; Jalilian, Yaghoub; Trujillo, Juan J.
2012
Maximum principle and its application for the time-fractional diffusion equations. Zbl 1273.35297
Luchko, Yury
2011
Fractional diffusion on bounded domains. Zbl 1488.35557
Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M.
2015
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. Zbl 1312.35184
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
2014
Uniqueness of solution for higher-order fractional differential equations with conjugate type integral conditions. Zbl 1395.34010
Zhang, Xingqiu; Zhong, Qiuyan
2017
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
2007
Strong maximum principle for fractional diffusion equations and an application to an inverse source problem. Zbl 1346.35216
Liu, Yikan; Rundell, William; Yamamoto, Masahiro
2016
Fuzzy fractional integral equations under compactness type condition. Zbl 1312.45009
2012
A brief story about the operators of the generalized fractional calculus. Zbl 1153.26003
Kiryakova, Virginia
2008
A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations. Zbl 1343.34006
Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal
2016
On the existence of blow up solutions for a class of fractional differential equations. Zbl 1312.34007
Bai, Zhanbing; Chen, YangQuan; Lian, Hairong; Sun, Sujing
2014
Linear models of dissipation whose $$Q$$ is almost frequency independent. II. (Reprint). Zbl 1210.65130
Caputo, Michele
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
2017
Fractional boundary value problems: analysis and numerical methods. Zbl 1273.65098
Ford, Neville J.; Morgado, M. Luísa
2011
Caputo-type modification of the Erdélyi-Kober fractional derivatives. Zbl 1152.26304
Luchko, Yury; Trujillo, Juan J.
2007
On the generalized Wright function. Zbl 1027.33015
Kilbas, Anatoly A.; Saigo, Megumi; Trujillo, Juan J.
2002
Erdélyi-Kober fractional diffusion. Zbl 1276.26021
Pagnini, Gianni
2012
Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications. Zbl 1381.35225
Liu, Zhenhai; Zeng, Shengda; Bai, Yunru
2016
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 06604016
Luchko, Yuri; Yamamoto, Masahiro
2016
Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions. Zbl 1321.49007
Debbouche, Amar; Torres, Delfim F. M.
2015
On $$q$$-analogues of Caputo derivative and Mittag-Leffler function. Zbl 1157.33325
Rajković, Predag M.; Marinković, Sladjana D.; Stanković, Miomir S.
2007
Subordination principle for fractional evolution equations. Zbl 1041.34046
Bazhlekova, Emilia G.
2000
High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. Zbl 1325.65121
Cao, Jianxiong; Li, Changpin; Chen, YangQuan
2015
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
2012
New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions. Zbl 1312.65166
Bhrawy, Ali; Alhamed, Yahia; Baleanu, Dumitru; Al-Zahrani, Abdulrahim
2014
On the asymptotic stability of linear system of fractional-order difference equations. Zbl 1312.39019
Abu-Saris, Raghib; Al-Mdallal, Qasem
2013
Nonpolynomial collocation approximation of solutions to fractional differential equations. Zbl 1312.65124
Ford, Neville J.; Morgado, M. Luísa; Rebelo, Magda
2013
A probabilistic interpretation of the fractional-order differentiation. Zbl 1035.26010
2003
Decay solutions for a class of fractional differential variational inequalities. Zbl 1319.49012
Dinh Ke, Tran; Van Loi, Nguyen; Obukhovskii, Valeri
2015
Positive solutions for a system of nonlocal fractional boundary value problems. Zbl 1312.34015
Henderson, Johnny; Luca, Rodica
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.
2008
Some pioneers of the applications of fractional calculus. Zbl 1305.26008
Valério, Duarte; Machado, José Tenreiro; Kiryakova, Virginia
2014
Models of dielectric relaxation based on completely monotone functions. Zbl 06663380
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
2016
Solving fractional delay differential equations: a new approach. Zbl 1317.34159
Daftardar-Gejji, Varsha; Sukale, Yogita; Bhalekar, Sachin
2015
Multiple solutions to boundary value problem for impulsive fractional differential equations. Zbl 1312.34024
Rodríguez-López, Rosana; Tersian, Stepan
2014
Well-posedness for the nonlinear fractional Schrödinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation. Zbl 1312.35180
Guo, Boling; Huo, Zhaohui
2013
Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions. Zbl 1279.34007
Graef, John R.; Kong, Lingju; Kong, Qingkai; Wang, Min
2012
High-order algorithms for Riesz derivative and their applications. III. Zbl 1332.65122
Ding, Hengfei; Li, Changpin
2016
Monotone iterative method for a class of nonlinear fractional differential equations. Zbl 1273.34021
Wang, Guotao; Baleanu, Dumitru; Zhang, Lihong
2012
Historical survey: the chronicles of fractional calculus. Zbl 1364.26002
Machado, J. A. Tenreiro; Kiryakova, Virginia
2017
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
2014
Hardy inequality in variable exponent Lebesgue spaces. Zbl 1132.26341
Diening, Lars; Samko, Stefan
2007
A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels. Zbl 1376.65159
2017
Existence and uniqueness of solutions for a fractional boundary value problem on a graph. Zbl 1308.34012
Graef, John R.; Kong, Lingju; Wang, Min
2014
Fractional differential inclusions with fractional separated boundary conditions. Zbl 1279.34003
2012
On existence and uniqueness of solutions for semilinear fractional wave equations. Zbl 1362.35323
Kian, Yavar; Yamamoto, Masahiro
2017
Initial-boundary value problems for fractional diffusion equations with time-dependent coefficients. Zbl 1398.35271
2018
A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures. Zbl 1312.76058
Chen, Wen; Zhang, Jianjun; Zhang, Jinyang
2013
Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces. Zbl 1312.47095
2013
Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data. Zbl 1333.65111
Jin, Bangti; Lazarov, Raytcho; Sheen, Dongwoo; Zhou, Zhi
2016
From fractal robustness to the CRONE control. Zbl 1111.93310
Oustaloup, Alain; Sabatier, Jocelyn; Lanusse, Patrick
1999
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
2010
An efficient parallel algorithm for the numerical solution of fractional differential equations. Zbl 1273.65101
Diethelm, Kai
2011
Fractional calculus of variations for a combined Caputo derivative. Zbl 1273.49025
Malinowska, Agnieszka B.; Torres, Delfim F. M.
2011
And I say to myself: “What a fractional world!”. Zbl 1273.37002
2011
Local and global existence of mild solutions for a class of semilinear fractional integro-differential equations. Zbl 1392.45016
Zhu, Bo; Liu, Lishan; Wu, Yonghong
2017
Fractional calculus of the generalized Wright function. Zbl 1144.26008
Kilbas, Anatoly A.
2005
Eigenvalue comparison for fractional boundary value problems with the Caputo derivative. Zbl 1310.34007
Henderson, Johnny; Kosmatov, Nickolai
2014
Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators. Zbl 1441.34006
Chen, Pengyu; Zhang, Xuping; Li, Yongxiang
2020
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
2010
An efficient localized collocation solver for anomalous diffusion on surfaces. Zbl 07382483
Tang, Zhuochao; Fu, Zhuojia; Sun, HongGuang; Liu, Xiaoting
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
2021
Towards a unified theory of fractional and nonlocal vector calculus. Zbl 07443850
D&rsquo;Elia, Marta; Gulian, Mamikon; Olson, Hayley; Karniadakis, George Em
2021
Operational calculus for the general fractional derivative and its applications. Zbl 07382460
Luchko, Yuri
2021
An inverse problem approach to determine possible memory length of fractional differential equations. Zbl 07443878
Gu, Chuan-Yun; Wu, Guo-Cheng; Shiri, Babak
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
2021
Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications. Zbl 07382467
2021
Three representations of the fractional $$p$$-Laplacian: semigroup, extension and Balakrishnan formulas. Zbl 07414209
del Teso, Félix; Gómez-Castro, David; Vázquez, Juan Luis
2021
Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives. Zbl 07337087
Bazhlekova, Emilia
2021
Stability analysis for discrete time abstract fractional differential equations. Zbl 1488.39059
He, Jia Wei; Zhou, Yong
2021
Existence of local solutions for fractional difference equations with left focal boundary conditions. Zbl 07337096
Henderson, Johnny; Neugebauer, Jeffrey T.
2021
Characterizations of variable martingale Hardy spaces via maximal functions. Zbl 07382462
Weisz, Ferenc
2021
Analysis of solutions of some multi-term fractional Bessel equations. Zbl 07443852
Dubovski, Pavel B.; Slepoi, Jeffrey
2021
Discrete fractional boundary value problems and inequalities. Zbl 07443872
Bohner, Martin; Fewster-Young, Nick
2021
The bouncing ball and the Grünwald-Letnikov definition of fractional derivative. Zbl 07414210
2021
Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity. Zbl 07414215
Hai, Dinh Nguyen Duy
2021
Maximum principles and applications for fractional differential equations with operators involving Mittag-Leffler function. Zbl 07414219
Al-Refai, Mohammed
2021
On the asymptotics of Wright functions of the second kind. Zbl 1474.30015
Paris, Richard B.; Consiglio, Armando; Mainardi, Francesco
2021
Error analysis of nonlinear time fractional mobile/immobile advection-diffusion equation with weakly singular solutions. Zbl 1488.65314
Zhang, Hui; Jiang, Xiaoyun; Liu, Fawang
2021
Monte Carlo estimation of the solution of fractional partial differential equations. Zbl 1488.65533
Kolokoltsov, Vassili; Lin, Feng; Mijatović, Aleksandar
2021
Contributions on artificial potential field method for effective obstacle avoidance. Zbl 07382463
Duhé, Jean-François; Victor, Stéphane; Melchior, Pierre
2021
Self-similar Cauchy problems and generalized Mittag-Leffler functions. Zbl 07382464
Patie, Pierre; Srapionyan, Anna
2021
Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives. Zbl 07382465
Kassim, Mohammed D.; Tatar, Nasser-eddine
2021
Galerkin method for time fractional semilinear equations. Zbl 07382479
Ouedjedi, Yamina; Rougirel, Arnaud; Benmeriem, Khaled
2021
Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation $$\partial_t^\beta u = -(-\Delta)^{\alpha /2}u -(-\Delta)^{\gamma /2}u$$. Zbl 07382481
Guerngar, Ngartelbaye; Nane, Erkan; Tinaztepe, Ramazan; Ulusoy, Suleyman; Van Wyk, Hans Werner
2021
Sliding methods for the higher order fractional Laplacians. Zbl 07382485
Wu, Leyun
2021
Green’s function for the fractional KdV equation on the periodic domain via Mittag-Leffler function. Zbl 07443856
Le, Uyen; Pelinovsky, Dmitry E.
2021
On the decomposition of solutions: from fractional diffusion to fractional Laplacian. Zbl 07443859
Li, Yulong
2021
Output error MISO system identification using fractional models. Zbl 07443860
Mayoufi, Abir; Victor, Stéphane; Chetoui, Manel; Malti, Rachid; Aoun, Mohamed
2021
Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations. Zbl 07443871
Zhang, Xuping; Chen, Pengyu; O&rsquo;Regan, Donal
2021
Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators. Zbl 1441.34006
Chen, Pengyu; Zhang, Xuping; Li, Yongxiang
2020
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco
2020
A comment on a controversial issue: a generalized fractional derivative cannot have a regular kernel. Zbl 1437.26010
Hanyga, Andrzej
2020
Why fractional derivatives with nonsingular kernels should not be used. Zbl 1474.26020
Diethelm, Kai; Garrappa, Roberto; Giusti, Andrea; Stynes, Martin
2020
Degenerate Kirchhoff $$(p, q)$$-fractional systems with critical nonlinearities. Zbl 1474.35054
Fiscella, Alessio; Pucci, Patrizia
2020
Attractivity for differential equations of fractional order and $$\psi$$-Hilfer type. Zbl 1488.34065
Sousa, J. Vanterler da C.; Benchohra, Mouffak; N&rsquo;Guérékata, Gaston M.
2020
On the kinetics of Hadamard-type fractional differential systems. Zbl 07241998
Ma, Li
2020
Determination of the order of fractional derivative for subdiffusion equations. Zbl 1474.35633
Ashurov, Ravshan; Umarov, Sabir
2020
On a non-local problem for a multi-term fractional diffusion-wave equation. Zbl 1446.35253
Ruzhansky, Michael; Tokmagambetov, Niyaz; Torebek, Berikbol T.
2020
Comments on: “The failure of certain fractional calculus operators in two physical models”. Zbl 1437.26008
Baleanu, Dumitru
2020
Well-posedness of the fractional Zener wave equation for heterogeneous viscoelastic materials. Zbl 1439.35544
Oparnica, Ljubica; Süli, Endre
2020
Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives. Zbl 1441.34009
Hanna, Latif A-M.; Al-Kandari, Maryam; Luchko, Yuri
2020
Stability of scalar nonlinear fractional differential equations with linearly dominated delay. Zbl 1441.34084
Tuan, Hoang The; Siegmund, Stefan
2020
An averaging principle for stochastic differential equations of fractional order $$0 < \alpha < 1$$. Zbl 1474.60168
Xu, Wenjing; Xu, Wei; Lu, Kai
2020
Two high-order time discretization schemes for subdiffusion problems with nonsmooth data. Zbl 1474.65293
Wang, Yanyong; Yan, Yubin; Yang, Yan
2020
A survey on numerical methods for spectral space-fractional diffusion problems. Zbl 1474.65438
Harizanov, Stanislav; Lazarov, Raytcho; Margenov, Svetozar
2020
Time-changed fractional Ornstein-Uhlenbeck process. Zbl 1450.60030
Ascione, Giacomo; Mishura, Yuliya; Pirozzi, Enrica
2020
Space-time fractional stochastic partial differential equations with Lévy noise. Zbl 1460.60066
Meng, Xiangqian; Nane, Erkan
2020
Solution of linear fractional order systems with variable coefficients. Zbl 1474.34047
Matychyn, Ivan; Onyshchenko, Viktoriia
2020
Inverse problem for a multi-term fractional differential equation. Zbl 1488.65379
Ali, Muhammad; Aziz, Sara; Malik, Salman A.
2020
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 1474.26024
Luchko, Yuri
2020
Multivariate fractional phase-type distributions. Zbl 1474.60025
2020
The continuation of solutions to systems of Caputo fractional order differential equations. Zbl 1451.34016
Wu, Cong; Liu, Xinzhi
2020
A note on models for anomalous phase-change processes. Zbl 1439.35573
Ceretani, Andrea N.
2020
Stability and resonance analysis of a general non-commensurate elementary fractional-order system. Zbl 1441.93211
Zhang, Shuo; Liu, Lu; Xue, Dingyu; Chen, YangQuan
2020
Fractional-order susceptible-infected model: definition and applications to the study of COVID-19 main protease. Zbl 1488.92024
2020
Generalized fractional Poisson process and related stochastic dynamics. Zbl 1474.60202
Michelitsch, Thomas M.; Riascos, Alejandro P.
2020
Maximum principles for a class of generalized time-fractional diffusion equations. Zbl 1488.35587
Zeng, Shengda; Migórski, Stanisław; Nguyen, Van Thien; Bai, Yunru
2020
On the harmonic extension approach to fractional powers in Banach spaces. Zbl 1474.47055
Meichsner, Jan; Seifert, Christian
2020
Analysis of fractional integro-differential equations with nonlocal Erdélyi-Kober type integral boundary conditions. Zbl 1488.45028
Duraisamy, Palanisamy; Gopal, Thangaraj Nandha; Subramanian, Muthaiah
2020
Regularity results for nonlocal evolution Venttsel’ problems. Zbl 1474.35358
Creo, Simone; Lancia, Maria Rosaria; Nazarov, Alexander I.
2020
A class of linear non-homogenous higher order matrix fractional differential equations: analytical solutions and new technique. Zbl 1451.34007
2020
Subordination principle for fractional diffusion-wave equations of Sobolev type. Zbl 1451.34014
Ponce, Rodrigo
2020
Fractional problems with critical nonlinearities by a sublinear perturbation. Zbl 1448.35195
Li, Lin; Tersian, Stepan
2020
New finite-time stability analysis of singular fractional differential equations with time-varying delay. Zbl 1453.34102
Thanh, Nguyen T.; Phat, Vu N.; Niamsup, Piyapong
2020
$$\alpha$$-fractionally convex functions. Zbl 1450.26003
Singha, Neelam; Nahak, Chandal
2020
Asymptotic stability of fractional difference equations with bounded time delays. Zbl 1448.26010
Wang, Mei; Jia, Baoguo; Du, Feifei; Liu, Xiang
2020
Crossover dynamics from superdiffusion to subdiffusion: models and solutions. Zbl 1439.35519
2020
The Green function for a class of Caputo fractional differential equations with a convection term. Zbl 1474.34200
Bai, Zhanbing; Sun, Sujing; Du, Zengji; Chen, YangQuan
2020
Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method. Zbl 1474.35641
Daoues, Adel; Hammami, Amani; Saoudi, Kamel
2020
Nontrivial solutions of non-autonomous Dirichlet fractional discrete problems. Zbl 1488.39032
2020
Initial-value / nonlocal Cauchy problems for fractional differential equations involving $$\psi$$-Hilfer multivariable operators. Zbl 1488.34048
Liang, Jin; Mu, Yunyi; Xiao, Ti-Jun
2020
Fractional abstract Cauchy problem on complex interpolation scales. Zbl 1474.35663
Lopushansky, Andriy; Lopushansky, Oleh; Szpila, Anna
2020
On representation formulas for solutions of linear differential equations with Caputo fractional derivatives. Zbl 1488.34036
Gomoyunov, Mikhail I.
2020
Integrability properties of integral transforms via Morrey spaces. Zbl 1472.46031
Samko, Natasha
2020
Fractional integro-differential equations in Wiener spaces. Zbl 1467.45019
Tuan, Vu Kim
2020
Trace inequalities for fractional integrals in mixed norm grand Lebesgue spaces. Zbl 1488.46061
Kokilashvili, Vakhtang; Meskhi, Alexander
2020
Cauchy problem for general time fractional diffusion equation. Zbl 1474.35672
Sin, Chung-Sik
2020
Wave propagation dynamics in a fractional Zener model with stochastic excitation. Zbl 1488.35324
Atanacković, Teodor; Pilipović, Stevan; Seleši, Dora
2020
Multidimensional van der Corput-type estimates involving Mittag-Leffler functions. Zbl 1473.42020
Ruzhansky, Michael; Torebek, Berikbol T.
2020
Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data. Zbl 1474.35693
Janno, Jaan
2020
Uniqueness for an inverse source problem of determining a space-dependent source in a non-autonomous time-fractional diffusion equation. Zbl 1474.35701
Slodička, Marian
2020
Nakhushev extremum principle for a class of integro-differential operators. Zbl 1474.26027
Pskhu, Arsen
2020
Implementation of fractional optimal control problems in real-world applications. Zbl 1488.92003
Singha, Neelam
2020
Fractional derivatives and Cauchy problem for differential equations of fractional order. Translation into English of the original paper [the authors, Izv. Akad. Nauk Arm. SSR, Mat. 3, 3–29 (1968; Zbl 0165.40801)]. Zbl 1474.35018
Dzherbashian, M. M.; Nersesian, A. B.
2020
Global existence and large time behavior of solutions of a time fractional reaction diffusion system. Zbl 1446.35244
Alsaedi, Ahmed; Ahmad, Bashir; Kirane, Mokhtar; Lassoued, Rafika
2020
A note on vanishing Morrey $$\rightarrow$$ VMO result for fractional integrals of variable order. Zbl 1453.46023
Rafeiro, Humberto; Samko, Stefan
2020
Determination of the fractional order in semilinear subdiffusion equations. Zbl 1474.35660
Krasnoschok, Mykola; Pereverzyev, Sergei; Siryk, Sergii V.; Vasylyeva, Nataliya
2020
“Fuzzy” calculus: the link between quantum mechanics and discrete fractional operators. Zbl 1474.26025
Nigmatullin, Raoul R.; Lino, Paolo; Maione, Guido
2020
Variational approximation for fractional Sturm-Liouville problem. Zbl 1488.34205
Pandey, Prashant K.; Pandey, Rajesh K.; Agrawal, Om P.
2020
Erdélyi-Kober fractional integrals and Radon transforms for mutually orthogonal affine planes. Zbl 1462.44003
Rubin, Boris; Wang, Yingzhan
2020
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications. Zbl 1428.34001
Sun, HongGuang; Chang, Ailian; Zhang, Yong; Chen, Wen
2019
Fractional impulsive differential equations: exact solutions, integral equations and short memory case. Zbl 1428.34025
Wu, Guo-Cheng; Zeng, De-Qiang; Baleanu, Dumitru
2019
Well-posedness of time-fractional advection-diffusion-reaction equations. Zbl 1439.35542
McLean, William; Mustapha, Kassem; Ali, Raed; Knio, Omar
2019
Some further results of the Laplace transform for variable-order fractional difference equations. Zbl 1439.65223
Baleanu, Dumitru; Wu, Guo-Cheng
2019
A system of coupled multi-term fractional differential equations with three-point coupled boundary conditions. Zbl 1428.34006
Ahmad, Bashir; Alghamdi, Najla; Alsaedi, Ahmed; Ntouya, Sotiris K.
2019
Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order $$1 < \alpha < 2$$. Zbl 1441.93038
Shu, Linxin; Shu, Xiao-Bao; Mao, Jianzhong
2019
Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations. Zbl 1423.35402
Kirane, Mokhtar; Torebek, Berikbol T.
2019
Finite element approximations for fractional evolution problems. Zbl 1426.65145
Acosta, Gabriel; Bersetche, Francisco M.; Borthagaray, Juan Pablo
2019
On Riesz derivative. Zbl 1426.26010
Cai, Min; Li, Changpin
2019
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