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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

46 Publications have been cited 2,611 times in 1,769 Documents Cited by Year
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
421
2001
Fractional differential equations. Zbl 1410.26004
216
2019
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
143
1999
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
138
2000
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
135
2002
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
133
2012
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
130
1998
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 1499.35642
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
126
2015
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
91
2013
Basic theory. Zbl 1410.26003
84
2019
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
69
1999
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 1499.35667
Luchko, Yuri; Yamamoto, Masahiro
62
2016
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
62
2013
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
60
2014
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
58
2000
Numerical solutions of linear multi-term initial value problems of fractional order. Zbl 1083.65064
Diethelm, Kai; Luchko, Yuri
57
2004
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
52
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
50
2013
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
47
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
47
2017
Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives. Zbl 1338.35457
Al-Refai, Mohammed; Luchko, Yuri
46
2015
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
36
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
34
2013
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
32
2013
Operational calculus for the general fractional derivative and its applications. Zbl 1498.26013
Luchko, Yuri
30
2021
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
27
1997
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
27
2014
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
26
2016
Wave-diffusion dualism of the neutral-fractional processes. Zbl 1349.35402
Luchko, Yuri
21
2015
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
20
2016
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 1474.26024
Luchko, Yuri
19
2020
On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Zbl 1474.35666
Luchko, Yuri
18
2017
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
Boyadjiev, Lyubomir; 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.
17
2016
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
11
2019
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
11
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
11
2022
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
8
2016
Convolution series and the generalized convolution Taylor formula. Zbl 1503.26012
Luchko, Yuri
8
2022
The neutral-fractional telegraph equation. Zbl 1398.35262
Boyadjiev, L.; Luchko, Yu.
6
2017
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 maximum principle for the multi-term fractional transport equation. Zbl 1475.35092
Luchko, Yuri; Suzuki, Anna; Yamamoto, Masahiro
4
2022
On the distribution of zeros of the Wright function. Zbl 1057.33014
Luchko, Yuri
4
2001
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
General fractional integrals and derivatives and their applications. Zbl 07767789
Luchko, Yuri
1
2023
General fractional integrals and derivatives and their applications. Zbl 07767789
Luchko, Yuri
1
2023
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
11
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
4
2022
Operational calculus for the general fractional derivative and its applications. Zbl 1498.26013
Luchko, Yuri
30
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
19
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
216
2019
Basic theory. Zbl 1410.26003
84
2019
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
11
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
47
2017
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
36
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
18
2017
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
Boyadjiev, Lyubomir; 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
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
62
2016
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
26
2016
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
20
2016
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
17
2016
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
8
2016
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 1499.35642
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
126
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
46
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
60
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
47
2014
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
27
2014
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
91
2013
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
62
2013
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
52
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
50
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
34
2013
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
32
2013
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
133
2012
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
11
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
135
2002
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
421
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
138
2000
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
58
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
143
1999
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
69
1999
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
130
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 2,109 Authors

39 Băleanu, Dumitru I.
39 Mainardi, Francesco
36 Liu, Fawang
36 Yamamoto, Masahiro
29 Luchko, Yuri
28 Zheng, Xiangcheng
25 Fernandez, Arran
23 Turner, Ian William
23 Wang, Hong
22 Pagnini, Gianni
21 Nguyen Huy Tuan
20 Li, Zhiyuan
19 Gorenflo, Rudolf
19 Povstenko, Yuriy Z.
18 Anh, Vo V.
17 Zhou, Yong
17 Zhou, Zhi
16 Garrappa, Roberto
15 Al-Refai, Mohammed
15 Sun, Zhizhong
15 Tarasov, Vasily E.
15 Zaky, Mahmoud A.
14 Ansari, Alireza
14 Jin, Bangti
14 Luchko, Yurii F.
13 Kian, Yavar
13 Liu, Yikan
13 Wang, Jinrong
12 Machado, José António Tenreiro
12 Sandev, Trifce
12 Saxena, Ram Kishore
12 Tomovski, Živorad
12 Wei, Ting
11 Ashurov, Ravshan Rajabovich
11 Malik, Salman A.
11 Roscani, Sabrina D.
11 Sin, Chung-Sik
11 Stynes, Martin Joseph
10 Hendy, Ahmed S.
10 Jiang, Xiaoyun
10 Lizama, Carlos
9 Bazhlekova, Emilia G.
9 Ford, Neville J.
9 Kirane, Mokhtar
9 Li, Xiaoxiao
9 Odibat, Zaid M.
9 Płociniczak, Łukasz
9 Pskhu, Arsen Vladimirovich
9 Tang, Yifa
9 Yang, Xuehua
9 Zhang, Haixiang
8 Abdel-Rehim, Entsar A.
8 Abdeljawad, Thabet
8 Atanackovic, Teodor M.
8 Beghin, Luisa
8 Bu, Weiping
8 Chechkin, Aleksei V.
8 Gómez-Aguilar, José Francisco
8 Hai, Dinh Nguyen Duy
8 Kaminski Lenzi, Ervin
8 Khushtova, Fatima Gidovna
8 Kiryakova, Virginia S.
8 Li, Gongsheng
8 Rogosin, Sergei V.
8 Singla, Komal
8 Sun, Liangliang
8 Yang, Fan
8 Zhang, Zhiyong
7 de Oliveira, Edmundo Capelas
7 D’Ovidio, Mirko
7 Ferreira, Milton
7 Haubold, Hans Joachim
7 Kolokoltsov, Vassili N.
7 Li, Miao
7 Lin, Guoxing
7 Mathai, Arakaparampli Mathai
7 Meerschaert, Mark Marvin
7 Metzler, Ralf
7 Momani, Shaher M.
7 O’Regan, Donal
7 Suragan, Durvudkhan
7 Tarzia, Domingo Alberto
7 Trong, Dang Duc
7 Umarov, Sabir R.
7 van Bockstal, Karel
7 Vieira, Nelson
7 Zhang, Zhidong
7 Zheng, Guanghui
6 Alikhanov, Anatoliĭ Alievich
6 Atangana, Abdon
6 Chen, Yangquan
6 Duan, Junsheng
6 Gao, Guanghua
6 Garra, Roberto
6 Górska, Katarzyna
6 Gupta, Rajesh Kumar
6 He, Jiawei
6 Hofmann, Bernd
6 Huang, Xinchi
6 Keyantuo, Valentin
...and 2,009 more Authors
all top 5

Cited in 324 Serials

203 Fractional Calculus & Applied Analysis
64 Mathematical Methods in the Applied Sciences
62 Journal of Computational and Applied Mathematics
61 Applied Mathematics and Computation
58 Computers & Mathematics with Applications
56 Communications in Nonlinear Science and Numerical Simulation
37 Advances in Difference Equations
34 Physica A
33 Chaos, Solitons and Fractals
32 Computational and Applied Mathematics
30 Journal of Mathematical Physics
29 Journal of Computational Physics
28 Inverse Problems
28 Journal of Scientific Computing
26 Journal of Mathematical Analysis and Applications
25 Applied Numerical Mathematics
22 Integral Transforms and Special Functions
21 Nonlinear Dynamics
19 Mathematics and Computers in Simulation
17 Applied Mathematics Letters
17 Journal of Applied Mathematics and Computing
15 Numerical Algorithms
14 Journal of Differential Equations
14 Journal of Inverse and Ill-Posed Problems
13 Numerical Methods for Partial Differential Equations
13 Abstract and Applied Analysis
13 Lobachevskii Journal of Mathematics
12 Applied Mathematical Modelling
12 International Journal of Computer Mathematics
12 Mathematical Problems in Engineering
12 Inverse Problems in Science and Engineering
11 Mathematics
11 Journal of Function Spaces
10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
10 Stochastic Processes and their Applications
10 International Journal of Differential Equations
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 Functional Analysis
7 Annals of Physics
7 Advances in Computational Mathematics
7 Journal of Evolution Equations
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 Reports on Mathematical Physics
6 BIT
6 Physica D
6 Journal of Mathematical Sciences (New York)
6 Communications on Pure and Applied Analysis
6 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
6 Journal of Nonlinear Science and Applications
6 International Journal of Applied and Computational Mathematics
6 AIMS Mathematics
5 Journal of Statistical Physics
5 Physics Letters. A
5 SIAM Journal on Mathematical Analysis
5 Turkish Journal of Mathematics
5 International Journal of Geometric Methods in Modern Physics
5 Mediterranean Journal of Mathematics
5 Mathematical Modelling of Natural Phenomena
5 Electronic Research Archive
4 Acta Mechanica
4 Computer Physics Communications
4 Lithuanian Mathematical Journal
4 Calcolo
4 Monatshefte für Mathematik
4 Semigroup Forum
4 Acta Mathematicae Applicatae Sinica. English Series
4 Journal of Integral Equations and Applications
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 Waves in Random and Complex Media
4 Complex Analysis and Operator Theory
4 Chinese Journal of Physics (Taipei)
4 Discrete and Continuous Dynamical Systems. Series S
4 Tbilisi Mathematical Journal
4 Ufimskiĭ Matematicheskiĭ Zhurnal
4 Axioms
4 Journal of Mathematics
3 Advances in Applied Probability
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
...and 224 more Serials
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Cited in 51 Fields

1,100 Partial differential equations (35-XX)
580 Real functions (26-XX)
518 Numerical analysis (65-XX)
313 Ordinary differential equations (34-XX)
242 Special functions (33-XX)
182 Probability theory and stochastic processes (60-XX)
163 Integral equations (45-XX)
138 Operator theory (47-XX)
103 Integral transforms, operational calculus (44-XX)
72 Fluid mechanics (76-XX)
62 Statistical mechanics, structure of matter (82-XX)
49 Mechanics of deformable solids (74-XX)
45 Quantum theory (81-XX)
43 Classical thermodynamics, heat transfer (80-XX)
41 Calculus of variations and optimal control; optimization (49-XX)
35 Systems theory; control (93-XX)
31 Functions of a complex variable (30-XX)
31 Harmonic analysis on Euclidean spaces (42-XX)
29 Biology and other natural sciences (92-XX)
26 Dynamical systems and ergodic theory (37-XX)
22 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
21 Functional analysis (46-XX)
18 Approximations and expansions (41-XX)
15 Statistics (62-XX)
14 Information and communication theory, circuits (94-XX)
13 Mechanics of particles and systems (70-XX)
12 Optics, electromagnetic theory (78-XX)
11 Global analysis, analysis on manifolds (58-XX)
8 Linear and multilinear algebra; matrix theory (15-XX)
7 Topological groups, Lie groups (22-XX)
7 Potential theory (31-XX)
7 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 Group theory and generalizations (20-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Computer science (68-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)
1 General and overarching topics; collections (00-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Field theory and polynomials (12-XX)
1 Commutative algebra (13-XX)
1 Algebraic geometry (14-XX)
1 Abstract harmonic analysis (43-XX)
1 Mathematics education (97-XX)

Citations by Year