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Luchko, Yuri

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Author ID: luchko.yuri Recent zbMATH articles by "Luchko, Yuri"
Published as: Luchko, Yuri; Luchko, Yu.
Documents Indexed: 44 Publications since 1997, including 3 Books
Reviewing Activity: 25 Reviews

Publications by Year

Citations contained in zbMATH Open

39 Publications have been cited 1,522 times in 1,064 Documents Cited by Year
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
316
2001
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
121
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
104
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
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
83
1998
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
73
2015
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
64
2012
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
57
2013
Numerical solutions of linear multi-term initial value problems of fractional order. Zbl 1083.65064
Diethelm, Kai; Luchko, Yuri
48
2004
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
44
2000
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
44
2013
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
42
1999
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
41
2014
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
38
2013
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 06604016
Luchko, Yuri; Yamamoto, Masahiro
33
2016
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications. Zbl 1305.34006
Al-Refai, Mohammed; Luchko, Yuri
32
2014
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
31
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
30
2015
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
25
2013
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
24
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
23
2013
Wave-diffusion dualism of the neutral-fractional processes. Zbl 1349.35402
Luchko, Yuri
18
2015
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
17
2017
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
13
1997
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
13
2016
On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Zbl 06898705
Luchko, Yuri
11
2017
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
11
2014
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
11
2016
Multi-dimensional \(\alpha\)-fractional diffusion-wave equation and some properties of its fundamental solution. Zbl 1386.35427
Boyadjiev, Lyubomir; Luchko, Yuri
10
2017
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
9
2016
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
7
2012
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
Boyadjiev, Lyubomir; Luchko, Yuri
6
2017
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
5
2016
The neutral-fractional telegraph equation. Zbl 1398.35262
Boyadjiev, L.; Luchko, Yu.
3
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
3
2020
Basic theory. Zbl 1410.26003
Kochubei, Anatoly (ed.); Luchko, Yuri (ed.)
3
2019
On the distribution of zeros of the Wright function. Zbl 1057.33014
Luchko, Yuri
2
2001
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 07268213
Luchko, Yuri
2
2020
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
1
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
3
2020
Fractional derivatives and the fundamental theorem of fractional calculus. Zbl 07268213
Luchko, Yuri
2
2020
Basic theory. Zbl 1410.26003
Kochubei, Anatoly; Luchko, Yuri
3
2019
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation. Zbl 1461.35007
Luchko, Yu.
1
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
24
2017
On the maximum principle for a time-fractional diffusion equation. Zbl 1374.35426
Luchko, Yuri; Yamamoto, Masahiro
17
2017
On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Zbl 06898705
Luchko, Yuri
11
2017
Multi-dimensional \(\alpha\)-fractional diffusion-wave equation and some properties of its fundamental solution. Zbl 1386.35427
Boyadjiev, Lyubomir; Luchko, Yuri
10
2017
Mellin integral transform approach to analyze the multidimensional diffusion-wave equations. Zbl 1374.35419
Boyadjiev, Lyubomir; Luchko, Yuri
6
2017
The neutral-fractional telegraph equation. Zbl 1398.35262
Boyadjiev, L.; Luchko, Yu.
3
2017
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Zbl 06604016
Luchko, Yuri; Yamamoto, Masahiro
33
2016
Modeling of financial processes with a space-time fractional diffusion equation of varying order. Zbl 1354.91178
Korbel, Jan; Luchko, Yuri
13
2016
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
11
2016
Analysis of fractional diffusion equations of distributed order: maximum principles and their applications. Zbl 1381.35208
Al-Refai, Mohammed; Luchko, Yuri
9
2016
Entropy production rate of a one-dimensional alpha-fractional diffusion process. Zbl 1415.35283
Luchko, Yuri
5
2016
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
73
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
30
2015
Wave-diffusion dualism of the neutral-fractional processes. Zbl 1349.35402
Luchko, Yuri
18
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
41
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
32
2014
Multi-dimensional fractional wave equation and some properties of its fundamental solution. Zbl 1329.35335
Luchko, Yuri
11
2014
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
57
2013
Fractional wave equation and damped waves. Zbl 1302.35408
Luchko, Yuri
44
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
38
2013
Fractional Schrödinger equation for a particle moving in a potential well. Zbl 1280.81044
Luchko, Yuri
31
2013
The Mellin integral transform in fractional calculus. Zbl 1312.26016
Luchko, Yuri; Kiryakova, Virginia
25
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
23
2013
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Zbl 1276.26018
Luchko, Yuri
64
2012
Complex oscillations and limit cycles in autonomous two-component incommensurate fractional dynamical systems. Zbl 1275.26015
Datsko, Bohdan; Luchko, Yuri
7
2012
Numerical solutions of linear multi-term initial value problems of fractional order. Zbl 1083.65064
Diethelm, Kai; Luchko, Yuri
48
2004
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
104
2002
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
316
2001
On the distribution of zeros of the Wright function. Zbl 1057.33014
Luchko, Yuri
2
2001
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
121
2000
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
44
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
104
1999
Operational method in fractional calculus. Zbl 1030.26009
Luchko, Yuri
42
1999
Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. Zbl 0932.58038
Buckwar, Evelyn; Luchko, Yuri
83
1998
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
13
1997
all top 5

Cited by 1,317 Authors

32 Liu, Fawang
32 Mainardi, Francesco
22 Băleanu, Dumitru I.
21 Luchko, Yuri
20 Turner, Ian William
19 Pagnini, Gianni
18 Gorenflo, Rudolf
17 Anh, Vo V.
17 Povstenko, Yuriy Z.
17 Yamamoto, Masahiro
14 Nguyen Huy Tuan
13 Wang, Jinrong
12 Garrappa, Roberto
12 Luchko, Yurii F.
12 Sun, Zhizhong
11 Li, Zhiyuan
11 Saxena, Ram Kishore
10 Wang, Hong
10 Zheng, Xiangcheng
9 Jin, Bangti
9 Odibat, Zaid M.
9 Sandev, Trifce
9 Stynes, Martin
8 Al-Refai, Mohammed
8 Kirane, Mokhtar
8 Roscani, Sabrina D.
8 Singla, Komal
8 Tomovski, Živorad
7 Bazhlekova, Emilia G.
7 Ford, Neville J.
7 Kiryakova, Virginia S.
7 Machado, José António Tenreiro
7 Mathai, Arakaparampli Mathai
7 Momani, Shaher M.
7 O’Regan, Donal
7 Tang, Yifa
7 Zaky, Mahmoud A.
7 Zhou, Zhi
6 Abdeljawad, Thabet
6 Ansari, Alireza
6 Bhalekar, Sachin
6 Bu, Weiping
6 de Oliveira, Edmundo Capelas
6 Chechkin, Aleksei V.
6 Gao, Guanghua
6 Gupta, Rajesh Kumar
6 Haubold, Hans Joachim
6 Hofmann, Bernd
6 Kaminski Lenzi, Ervin
6 Lazarov, Raytcho D.
6 Li, Gongsheng
6 Lizama, Carlos
6 Meerschaert, Mark Marvin
6 Płociniczak, Łukasz
6 Popolizio, Marina
6 Sin, Chung-Sik
5 Chen, Yangquan
5 D’Ovidio, Mirko
5 Duan, Junsheng
5 Gómez-Aguilar, José Francisco
5 Hai, Dinh Nguyen Duy
5 Jarad, Fahd
5 Jia, Junxiong
5 Jiang, Xiaoyun
5 Keyantuo, Valentin
5 Kienle, Alwin
5 Liemert, André
5 Polito, Federico
5 Sahadevan, Ramajayam
5 Sun, Chunlong
5 Tarzia, Domingo Alberto
5 Trong, Dang Duc
5 Trujillo, Juan J.
5 Umarov, Sabir R.
5 Wang, Gangwei
5 Xu, Mingyu
5 Yang, Xiao-Jun
5 Yang, Xuehua
5 Zhang, Haixiang
4 Al-saedi, Ahmed Eid Salem
4 Arshad, Muhammad Sarmad
4 Atanackovic, Teodor M.
4 Atangana, Abdon
4 Beghin, Luisa
4 Bhrawy, Ali Hassan
4 Boyadjiev, Lyubomir I.
4 Brandibur, Oana
4 Chen, Wen
4 Demir, Ali
4 El-Sayed, Ahmed Mohamed Ahmed
4 Esmaeili, Shahrokh
4 Feng, Libo
4 Ferreira, Milton
4 Garra, Roberto
4 Hanna, Latif A.-M.
4 Janno, Jaan
4 Kaslik, Eva
4 Khaliq, Abdul Q. M.
4 Kiliçman, Adem
4 Kolokoltsov, Vassili N.
...and 1,217 more Authors
all top 5

Cited in 228 Serials

131 Fractional Calculus & Applied Analysis
52 Applied Mathematics and Computation
50 Computers & Mathematics with Applications
49 Journal of Computational and Applied Mathematics
28 Journal of Mathematical Physics
26 Journal of Computational Physics
25 Communications in Nonlinear Science and Numerical Simulation
24 Advances in Difference Equations
21 Journal of Mathematical Analysis and Applications
20 Journal of Scientific Computing
20 Nonlinear Dynamics
19 Chaos, Solitons and Fractals
19 Applied Numerical Mathematics
18 Inverse Problems
16 Journal of Applied Mathematics and Computing
15 Integral Transforms and Special Functions
13 Computational and Applied Mathematics
13 Abstract and Applied Analysis
12 Applied Mathematics Letters
12 Numerical Algorithms
12 Mathematical Problems in Engineering
11 Mathematics
10 Physica A
10 International Journal of Differential Equations
9 Journal of Inverse and Ill-Posed Problems
8 Applied Mathematical Modelling
8 Advances in Mathematical Physics
7 Applicable Analysis
7 Journal of Differential Equations
7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
7 Stochastic Processes and their Applications
7 Lobachevskii Journal of Mathematics
7 Inverse Problems in Science and Engineering
6 Mathematical Methods in the Applied Sciences
6 SIAM Journal on Numerical Analysis
6 Boundary Value Problems
6 Journal of Nonlinear Science and Applications
5 BIT
5 Journal of Evolution Equations
5 Mathematical Modelling of Natural Phenomena
5 Journal of Function Spaces
4 Computer Methods in Applied Mechanics and Engineering
4 Journal of Statistical Physics
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik
4 Journal of Functional Analysis
4 Acta Mathematicae Applicatae Sinica. English Series
4 International Journal of Computer Mathematics
4 Engineering Analysis with Boundary Elements
4 Nonlinear Analysis. Modelling and Control
4 Journal of Applied Mathematics
4 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
4 Ufimskiĭ Matematicheskiĭ Zhurnal
4 Axioms
4 Journal of Mathematics
3 Acta Mechanica
3 Advances in Applied Probability
3 International Journal of Theoretical Physics
3 Lithuanian Mathematical Journal
3 Mathematics of Computation
3 Mathematics and Computers in Simulation
3 Meccanica
3 Semigroup Forum
3 Zeitschrift für Analysis und ihre Anwendungen
3 Physica D
3 Russian Mathematics
3 Journal of Mathematical Chemistry
3 Journal of Inequalities and Applications
3 Discrete and Continuous Dynamical Systems. Series B
3 Computational Methods in Applied Mathematics
3 International Journal of Geometric Methods in Modern Physics
3 Inverse Problems and Imaging
3 Tbilisi Mathematical Journal
3 Symmetry
3 Fractional Differential Calculus
3 Evolution Equations and Control Theory
3 East Asian Journal on Applied Mathematics
2 Mathematical Notes
2 Nonlinearity
2 Reports on Mathematical Physics
2 Theoretical and Mathematical Physics
2 Journal of Geometry and Physics
2 Calcolo
2 Journal of Optimization Theory and Applications
2 Monatshefte für Mathematik
2 Numerical Functional Analysis and Optimization
2 Proceedings of the American Mathematical Society
2 Quarterly of Applied Mathematics
2 Applied Mathematics and Mechanics. (English Edition)
2 Journal of Integral Equations and Applications
2 Signal Processing
2 SIAM Journal on Mathematical Analysis
2 SIAM Journal on Scientific Computing
2 Journal of Mathematical Sciences (New York)
2 International Journal of Numerical Methods for Heat & Fluid Flow
2 Journal of the Egyptian Mathematical Society
2 Fractals
2 Advances in Computational Mathematics
2 Journal of Vibration and Control
2 Taiwanese Journal of Mathematics
2 Mathematical Inequalities & Applications
...and 128 more Serials
all top 5

Cited in 49 Fields

640 Partial differential equations (35-XX)
339 Real functions (26-XX)
323 Numerical analysis (65-XX)
194 Ordinary differential equations (34-XX)
160 Special functions (33-XX)
118 Probability theory and stochastic processes (60-XX)
114 Integral equations (45-XX)
66 Operator theory (47-XX)
60 Integral transforms, operational calculus (44-XX)
48 Fluid mechanics (76-XX)
36 Statistical mechanics, structure of matter (82-XX)
34 Mechanics of deformable solids (74-XX)
33 Classical thermodynamics, heat transfer (80-XX)
28 Quantum theory (81-XX)
24 Calculus of variations and optimal control; optimization (49-XX)
19 Harmonic analysis on Euclidean spaces (42-XX)
19 Systems theory; control (93-XX)
17 Functions of a complex variable (30-XX)
16 Biology and other natural sciences (92-XX)
14 Dynamical systems and ergodic theory (37-XX)
11 Functional analysis (46-XX)
11 Statistics (62-XX)
10 Approximations and expansions (41-XX)
10 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
8 Mechanics of particles and systems (70-XX)
8 Information and communication theory, circuits (94-XX)
7 Global analysis, analysis on manifolds (58-XX)
7 Optics, electromagnetic theory (78-XX)
6 Topological groups, Lie groups (22-XX)
4 History and biography (01-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Measure and integration (28-XX)
4 Sequences, series, summability (40-XX)
3 Potential theory (31-XX)
3 Geophysics (86-XX)
2 Combinatorics (05-XX)
2 Group theory and generalizations (20-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Abstract harmonic analysis (43-XX)
2 Operations research, mathematical programming (90-XX)
1 General and overarching topics; collections (00-XX)
1 Mathematical logic and foundations (03-XX)
1 Field theory and polynomials (12-XX)
1 Algebraic geometry (14-XX)
1 Nonassociative rings and algebras (17-XX)
1 Difference and functional equations (39-XX)
1 Computer science (68-XX)
1 Relativity and gravitational theory (83-XX)
1 Mathematics education (97-XX)

Citations by Year