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Author ID: luchko.yuri Recent zbMATH articles by "Luchko, Yuri"
Published as: Luchko, Yuri; Luchko, Yu.

Publications by Year

Citations contained in zbMATH Open

45 Publications have been cited 2,321 times in 1,609 Documents Cited by Year
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
383
2001
Fractional differential equations. Zbl 1410.26004
138
2019
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
136
1999
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
132
2000
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
125
2012
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
125
2002
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
119
1998
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 1499.35642
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
118
2015
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
85
2013
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
64
1999
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
59
2013
Numerical solutions of linear multi-term initial value problems of fractional order. Zbl 1083.65064
Diethelm, Kai; Luchko, Yuri
57
2004
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
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
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
53
2000
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
47
2013
Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation. Zbl 1273.65131
Luchko, Yuri; Rundell, William; Yamamoto, Masahiro; Zuo, Lihua
47
2013
Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives. Zbl 1338.35457
Al-Refai, Mohammed; Luchko, Yuri
45
2015
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
44
2014
Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem. Zbl 1409.35221
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
43
2017
Basic theory. Zbl 1410.26003
42
2019
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
35
2017
Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226
Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy
33
2013
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
30
2013
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
27
1997
Operational calculus for the general fractional derivative and its applications. Zbl 1498.26013
Luchko, Yuri
26
2021
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
23
2016
Wave-diffusion dualism of the neutral-fractional processes. Zbl 1349.35402
Luchko, Yuri
21
2015
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
20
2014
On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Zbl 1474.35666
Luchko, Yuri
17
2017
Multi-dimensional \(\alpha\)-fractional diffusion-wave equation and some properties of its fundamental solution. Zbl 1386.35427
Boyadjiev, Lyubomir; Luchko, Yuri
17
2017
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
16
2016
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
Boyadjiev, Lyubomir; Luchko, Yuri
16
2017
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
16
2016
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 1474.26024
Luchko, Yuri
14
2020
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
9
2012
Comparison principles for solutions to the fractional differential inequalities with the general fractional derivatives and their applications. Zbl 1505.34007
Al-Refai, Mohammed; Luchko, Yuri
8
2022
Convolution series and the generalized convolution Taylor formula. Zbl 1503.26012
Luchko, Yuri
8
2022
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
7
2016
The neutral-fractional telegraph equation. Zbl 1398.35262
Boyadjiev, L.; Luchko, Yu.
6
2017
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
6
2019
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
6
2020
On the distribution of zeros of the Wright function. Zbl 1057.33014
Luchko, Yuri
4
2001
On the maximum principle for the multi-term fractional transport equation. Zbl 1475.35092
Luchko, Yuri; Suzuki, Anna; Yamamoto, Masahiro
3
2022
Multidimensional scaling and visualization of patterns in distribution of nontrivial zeros of the zeta-function. Zbl 1469.11298
Machado, J. Tenreiro; Luchko, Yuri
1
2021
Comparison principles for solutions to the fractional differential inequalities with the general fractional derivatives and their applications. Zbl 1505.34007
Al-Refai, Mohammed; Luchko, Yuri
8
2022
Convolution series and the generalized convolution Taylor formula. Zbl 1503.26012
Luchko, Yuri
8
2022
On the maximum principle for the multi-term fractional transport equation. Zbl 1475.35092
Luchko, Yuri; Suzuki, Anna; Yamamoto, Masahiro
3
2022
Operational calculus for the general fractional derivative and its applications. Zbl 1498.26013
Luchko, Yuri
26
2021
Multidimensional scaling and visualization of patterns in distribution of nontrivial zeros of the zeta-function. Zbl 1469.11298
Machado, J. Tenreiro; Luchko, Yuri
1
2021
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 1474.26024
Luchko, Yuri
14
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
6
2020
Fractional differential equations. Zbl 1410.26004
138
2019
Basic theory. Zbl 1410.26003
42
2019
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
6
2019
Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem. Zbl 1409.35221
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
43
2017
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
35
2017
On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Zbl 1474.35666
Luchko, Yuri
17
2017
Multi-dimensional \(\alpha\)-fractional diffusion-wave equation and some properties of its fundamental solution. Zbl 1386.35427
Boyadjiev, Lyubomir; Luchko, Yuri
17
2017
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
Boyadjiev, Lyubomir; Luchko, Yuri
16
2017
The neutral-fractional telegraph equation. Zbl 1398.35262
Boyadjiev, L.; Luchko, Yu.
6
2017
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 1499.35667
Luchko, Yuri; Yamamoto, Masahiro
56
2016
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
23
2016
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
16
2016
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
16
2016
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
7
2016
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 1499.35642
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
118
2015
Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives. Zbl 1338.35457
Al-Refai, Mohammed; Luchko, Yuri
45
2015
Wave-diffusion dualism of the neutral-fractional processes. Zbl 1349.35402
Luchko, Yuri
21
2015
Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. Zbl 1312.35184
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro
56
2014
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
44
2014
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
20
2014
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
85
2013
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
59
2013
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
47
2013
Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation. Zbl 1273.65131
Luchko, Yuri; Rundell, William; Yamamoto, Masahiro; Zuo, Lihua
47
2013
Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226
Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy
33
2013
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
30
2013
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
125
2012
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
9
2012
Numerical solutions of linear multi-term initial value problems of fractional order. Zbl 1083.65064
Diethelm, Kai; Luchko, Yuri
57
2004
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
125
2002
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
383
2001
On the distribution of zeros of the Wright function. Zbl 1057.33014
Luchko, Yuri
4
2001
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
132
2000
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
53
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
136
1999
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
64
1999
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
119
1998
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
27
1997
all top 5

Cited by 1,943 Authors

38 Mainardi, Francesco
35 Liu, Fawang
32 Yamamoto, Masahiro
31 Băleanu, Dumitru I.
29 Luchko, Yuri
24 Zheng, Xiangcheng
22 Turner, Ian William
21 Pagnini, Gianni
21 Wang, Hong
20 Fernandez, Arran
19 Gorenflo, Rudolf
19 Povstenko, Yuriy Z.
18 Li, Zhiyuan
18 Nguyen Huy Tuan
17 Anh, Vo V.
15 Garrappa, Roberto
15 Zhou, Zhi
14 Al-Refai, Mohammed
13 Jin, Bangti
13 Luchko, Yurii F.
13 Sun, Zhizhong
13 Wang, Jinrong
13 Zaky, Mahmoud A.
13 Zhou, Yong
11 Ansari, Alireza
11 Kian, Yavar
11 Liu, Yikan
11 Roscani, Sabrina D.
11 Saxena, Ram Kishore
11 Stynes, Martin Joseph
11 Wei, Ting
10 Ashurov, Ravshan Rajabovich
10 Jiang, Xiaoyun
10 Malik, Salman A.
10 Sandev, Trifce
10 Sin, Chung-Sik
10 Tarasov, Vasily E.
10 Tomovski, Živorad
9 Hendy, Ahmed S.
9 Kirane, Mokhtar
9 Machado, José António Tenreiro
9 Odibat, Zaid M.
9 Płociniczak, Łukasz
9 Pskhu, Arsen Vladimirovich
9 Yang, Xuehua
9 Zhang, Haixiang
8 Abdeljawad, Thabet
8 Bazhlekova, Emilia G.
8 Chechkin, Aleksei V.
8 Ford, Neville J.
8 Hai, Dinh Nguyen Duy
8 Khushtova, Fatima Gidovna
8 Kiryakova, Virginia S.
8 Li, Gongsheng
8 Lizama, Carlos
8 Singla, Komal
8 Sun, Liangliang
8 Tang, Yifa
7 Abdel-Rehim, Entsar A.
7 Bu, Weiping
7 de Oliveira, Edmundo Capelas
7 Kolokoltsov, Vassili N.
7 Li, Xiaoxiao
7 Meerschaert, Mark Marvin
7 Metzler, Ralf
7 Momani, Shaher M.
7 O’Regan, Donal
7 Rogosin, Sergei V.
7 Tarzia, Domingo Alberto
7 Trong, Dang Duc
7 Yang, Fan
7 Zhang, Zhidong
6 Alikhanov, Anatoliĭ Alievich
6 Atanackovic, Teodor M.
6 Beghin, Luisa
6 D’Ovidio, Mirko
6 Ferreira, Milton
6 Gao, Guanghua
6 Garra, Roberto
6 Gómez-Aguilar, José Francisco
6 Gupta, Rajesh Kumar
6 Haubold, Hans Joachim
6 Hofmann, Bernd
6 Huang, Xinchi
6 Kaminski Lenzi, Ervin
6 Lapin, Aleksandr Vasil’evich
6 Lazarov, Raytcho D.
6 Li, Hong
6 Li, Miao
6 Liu, Yang
6 Mathai, Arakaparampli Mathai
6 Popolizio, Marina
6 Sun, Chunlong
6 Suragan, Durvudkhan
6 Umarov, Sabir R.
6 van Bockstal, Karel
6 Vieira, Nelson
6 Xu, Da
6 Zhang, Zhiyong
5 Arshad, Muhammad
...and 1,843 more Authors
all top 5

Cited in 314 Serials

185 Fractional Calculus & Applied Analysis
61 Applied Mathematics and Computation
59 Journal of Computational and Applied Mathematics
55 Computers & Mathematics with Applications
37 Advances in Difference Equations
36 Communications in Nonlinear Science and Numerical Simulation
33 Chaos, Solitons and Fractals
29 Journal of Computational Physics
29 Journal of Mathematical Physics
28 Physica A
27 Mathematical Methods in the Applied Sciences
27 Journal of Scientific Computing
26 Computational and Applied Mathematics
25 Inverse Problems
25 Journal of Mathematical Analysis and Applications
25 Applied Numerical Mathematics
22 Integral Transforms and Special Functions
21 Nonlinear Dynamics
17 Applied Mathematics Letters
17 Journal of Applied Mathematics and Computing
15 Mathematics and Computers in Simulation
15 Numerical Algorithms
13 Journal of Differential Equations
13 Abstract and Applied Analysis
12 International Journal of Computer Mathematics
12 Journal of Inverse and Ill-Posed Problems
12 Mathematical Problems in Engineering
12 Lobachevskii Journal of Mathematics
12 Inverse Problems in Science and Engineering
11 Numerical Methods for Partial Differential Equations
11 Mathematics
10 Applied Mathematical Modelling
10 Stochastic Processes and their Applications
10 International Journal of Differential Equations
10 Journal of Function Spaces
9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
9 SIAM Journal on Numerical Analysis
9 Computational Methods in Applied Mathematics
9 Boundary Value Problems
9 Advances in Mathematical Physics
8 Applicable Analysis
8 Fractional Differential Calculus
7 ZAMP. Zeitschrift für angewandte Mathematik und Physik
7 Journal of Physics A: Mathematical and Theoretical
7 Inverse Problems and Imaging
7 Evolution Equations and Control Theory
6 Computer Methods in Applied Mechanics and Engineering
6 BIT
6 Physica D
6 Advances in Computational Mathematics
6 Journal of Evolution Equations
6 Communications on Pure and Applied Analysis
6 Journal of Nonlinear Science and Applications
6 International Journal of Applied and Computational Mathematics
6 AIMS Mathematics
5 Journal of Statistical Physics
5 Journal of Mathematical Sciences (New York)
5 Turkish Journal of Mathematics
5 Mediterranean Journal of Mathematics
5 Mathematical Modelling of Natural Phenomena
5 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
5 Electronic Research Archive
4 Lithuanian Mathematical Journal
4 Reports on Mathematical Physics
4 Calcolo
4 Journal of Functional Analysis
4 Monatshefte für Mathematik
4 Semigroup Forum
4 Acta Mathematicae Applicatae Sinica. English Series
4 Journal of Integral Equations and Applications
4 SIAM Journal on Mathematical Analysis
4 Russian Mathematics
4 Fractals
4 Engineering Analysis with Boundary Elements
4 Boletín de la Sociedad Matemática Mexicana. Third Series
4 Taiwanese Journal of Mathematics
4 The ANZIAM Journal
4 Nonlinear Analysis. Modelling and Control
4 Discrete and Continuous Dynamical Systems. Series B
4 Journal of Applied Mathematics
4 International Journal of Geometric Methods in Modern Physics
4 Waves in Random and Complex Media
4 Discrete and Continuous Dynamical Systems. Series S
4 Tbilisi Mathematical Journal
4 Ufimskiĭ Matematicheskiĭ Zhurnal
4 Axioms
4 Journal of Mathematics
3 Acta Mechanica
3 Advances in Applied Probability
3 Computer Physics Communications
3 International Journal of Theoretical Physics
3 Mathematical Notes
3 Ukrainian Mathematical Journal
3 Mathematics of Computation
3 Journal of Optimization Theory and Applications
3 Mathematische Nachrichten
3 Meccanica
3 Zeitschrift für Analysis und ihre Anwendungen
3 Statistics & Probability Letters
3 Annals of Physics
...and 214 more Serials
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Cited in 50 Fields

1,007 Partial differential equations (35-XX)
523 Real functions (26-XX)
479 Numerical analysis (65-XX)
278 Ordinary differential equations (34-XX)
225 Special functions (33-XX)
171 Probability theory and stochastic processes (60-XX)
154 Integral equations (45-XX)
123 Operator theory (47-XX)
93 Integral transforms, operational calculus (44-XX)
64 Fluid mechanics (76-XX)
53 Statistical mechanics, structure of matter (82-XX)
47 Mechanics of deformable solids (74-XX)
41 Classical thermodynamics, heat transfer (80-XX)
40 Quantum theory (81-XX)
36 Calculus of variations and optimal control; optimization (49-XX)
32 Systems theory; control (93-XX)
28 Functions of a complex variable (30-XX)
26 Harmonic analysis on Euclidean spaces (42-XX)
24 Dynamical systems and ergodic theory (37-XX)
24 Biology and other natural sciences (92-XX)
18 Functional analysis (46-XX)
17 Approximations and expansions (41-XX)
16 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
14 Statistics (62-XX)
11 Information and communication theory, circuits (94-XX)
10 Global analysis, analysis on manifolds (58-XX)
10 Optics, electromagnetic theory (78-XX)
9 Mechanics of particles and systems (70-XX)
8 Linear and multilinear algebra; matrix theory (15-XX)
7 Topological groups, Lie groups (22-XX)
7 Potential theory (31-XX)
6 Difference and functional equations (39-XX)
5 History and biography (01-XX)
5 Measure and integration (28-XX)
5 Geophysics (86-XX)
4 Number theory (11-XX)
4 Sequences, series, summability (40-XX)
3 Relativity and gravitational theory (83-XX)
3 Operations research, mathematical programming (90-XX)
2 Combinatorics (05-XX)
2 Nonassociative rings and algebras (17-XX)
2 Group theory and generalizations (20-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Computer science (68-XX)
1 General and overarching topics; collections (00-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Field theory and polynomials (12-XX)
1 Algebraic geometry (14-XX)
1 Abstract harmonic analysis (43-XX)
1 Mathematics education (97-XX)

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