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Author ID: gorenflo.rudolf Recent zbMATH articles by "Gorenflo, Rudolf"
Published as: Gorenflo, Rudolf; Gorenflo, R.; Gorenfloh, Rudolf
Homepage: http://www.math.berlin/nachrufe/rudolf-gorenflo.html
External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef
Documents Indexed: 146 Publications since 1961, including 4 Books
8 Contributions as Editor
Reviewing Activity: 233 Reviews
Biographic References: 4 Publications
Co-Authors: 80 Co-Authors with 124 Joint Publications
2,198 Co-Co-Authors
all top 5

Co-Authors

30 single-authored
40 Mainardi, Francesco
11 Ang, Dang Dinh
7 Kilbas, Anatoliĭ Aleksandrovich
7 Luchko, Yuri
7 Tran Duc Van
7 Vivoli, Alessandro
7 Vu Kim Tuan
6 Luchko, Yurii F.
6 Pagnini, Gianni
6 Yamamoto, Masahiro
5 Scalas, Enrico
4 Abdel-Rehim, Entsar A.
4 Đinh Nho Hào
4 Le, Vy Khoi
4 Rogosin, Sergei V.
4 Umarov, Sabir R.
3 Mura, Antonio
3 Raberto, Marco
3 Rutman, Roman S.
3 Stojanović, Mirjana N.
3 Vogel, Andreas
2 Chechkin, Aleksei V.
2 Hofmann, Bernd
2 Iskenderov, Asaf
2 Moretti, Daniele
2 Paradisi, Paolo
2 Pfeiffer, Andreas
2 Rubin, Boris
2 Sebastian, Nicy
2 Sokolov, Igor’ Mikhaĭlovich
2 Srivastava, Hari Mohan
2 Trong, Dang Duc
2 Yakubovich, Semyon B.
1 Anger, Gottfried
1 Berendt, Gerhard
1 Dang Dinh Hai
1 Dinh Dũng
1 Dinh Ngoc Thanh
1 Duong Minh Duc
1 Fleischer, Gunter
1 Garra, Roberto
1 Gonchar, Vsevolod Yu.
1 Gudehus, Gerd
1 Ha Huy Bang
1 Hilpert, Martin
1 Hoffmann, Karl-Heinz
1 Jochmann, Horst
1 Kiesner, Stefan
1 Kiryakova, Virginia S.
1 Kounchev, Ognyan Ivanov
1 Kovetz, Y.
1 Kuban, Angelika
1 Le Hung Son
1 Le Van Hap
1 Loutchko, Joulia
1 Luckock, Hugh
1 Mai Duc Thanh
1 Mantelli, Maurizio
1 Moritz, Helmut
1 Navarro, Milagros P.
1 Nguyen Quoc Son
1 Niedack, Marianne
1 Ofoegbu, Charles O.
1 Oldham, Keith B.
1 Pagani, Carlo Domenico
1 Pham Ky Anh
1 Polito, Federico
1 Saigo, Megumi
1 Samko, Stefan Grigorievich
1 Sarwar, Abu K. M.
1 Schaum, H. J.
1 Tautenhahn, Ulrich
1 Tomovski, Živorad
1 Touplikiotis, Asterios
1 Trinh Ngoc Minh
1 Ursin, Bjørn
1 Vessella, Sergio
1 Webers, Wigor
1 Yu Kim Tuan
1 Zabreĭko, Pëtr Petrovich
all top 5

Serials

17 Fractional Calculus & Applied Analysis
7 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
6 Journal of Computational and Applied Mathematics
5 Zeitschrift für Analysis und ihre Anwendungen
4 Vietnam Journal of Mathematics
3 Inverse Problems
3 Acta Mathematica Vietnamica
3 Numerical Functional Analysis and Optimization
3 Journal of Fractional Calculus
3 Journal of Inverse and Ill-Posed Problems
3 Integral Transforms and Special Functions
2 Matimyás Matematika
2 Applied Mathematics and Computation
2 Archiv der Mathematik
2 Computing
2 Numerische Mathematik
2 Analysis
2 Journal of Mathematical Sciences (New York)
2 Journal of Vibration and Control
2 Nonlinear Dynamics
2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
2 Lecture Notes in Mathematics
2 Springer Monographs in Mathematics
1 Applicable Analysis
1 Archives of Mechanics
1 Physica A
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Chaos, Solitons and Fractals
1 Annales Polonici Mathematici
1 Differential Equations
1 Mathematische Annalen
1 Acta Applicandae Mathematicae
1 Signal Processing
1 Japan Journal of Industrial and Applied Mathematics
1 Communications in Statistics. Theory and Methods
1 Journal of Physics A: Mathematical and General
1 Zeitschrift für Naturforschung. A. Physik, Physikalische Chemie, Kosmophysik
1 International Journal of Mathematical and Statistical Sciences
1 Theory of Probability and Mathematical Statistics
1 Fractals
1 Kuwait Journal of Science and Engineering
1 Analysis (München)
1 Nonlinear Analysis. Real World Applications
1 Quantitative Finance
1 Doklady Natsional’noĭ Akademii Nauk Belarusi
1 Communications in Applied and Industrial Mathematics
1 Axioms
1 Biometrische Zeitschrift
1 Nonlinear Analysis. Theory, Methods & Applications
1 Mathematical Research

Publications by Year

Citations contained in zbMATH Open

121 Publications have been cited 3,843 times in 2,647 Documents Cited by Year
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
462
2014
An operational method for solving fractional differential equations with the Caputo derivatives. Zbl 0931.44003
Luchko, Yurii; Gorenflo, Rudolf
173
1999
On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
173
2000
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
157
2002
Abel integral equations. Analysis and applications. Zbl 0717.45002
Gorenflo, Rudolf; Vessella, Sergio
153
1991
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
152
2001
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
134
1998
Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010
Gorenflo, R.; Mainardi, F.
132
1997
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
128
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
119
1999
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
114
2002
Fractional diffusion in inhomogeneous media. Zbl 1082.76097
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.
100
2005
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
90
2002
Distributed order time fractional diffusion equation. Zbl 1089.60046
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu.
89
2003
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
88
2015
Hilfer-Prabhakar derivatives and some applications. Zbl 1334.26008
Garra, Roberto; Gorenflo, Rudolf; Polito, Federico; Tomovski, Živorad
83
2014
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
77
2007
Time-fractional diffusion of distributed order. Zbl 1229.35118
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
76
2008
Fractional calculus: Special functions and applications. Zbl 1030.26004
Mainardi, F.; Gorenflo, R.
73
2000
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
72
2004
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
67
2013
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
64
2009
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
54
1998
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
51
2007
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
51
2000
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
47
2007
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
45
1998
Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
44
1996
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
43
2007
On the generalized Mittag-Leffler type functions. Zbl 0935.33012
Gorenflo, R.; Kilbas, A. A.; Rogosin, S. V.
42
1998
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
39
1999
Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations. I. Zbl 1100.35132
Umarov, Sabir; Gorenflo, Rudolf
36
2005
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
35
1998
Mittag-Leffler functions, related topics and applications. 2nd extended and updated edition. Zbl 1451.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
33
2020
On autoconvolution and regularization. Zbl 0804.45003
Gorenflo, Rudolf; Hofmann, Bernd
30
1994
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
27
2003
Operator theoretic treatment of linear Abel integral equations of first kind. Zbl 1306.47057
Gorenflo, Rudolf; Yamamoto, Masahiro
25
1999
Extrapolation to the limit for numerical fractional differentiation. Zbl 0860.65011
Vu Kim Tuan; Gorenflo, R.
21
1995
Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
21
2005
On ultraslow and intermediate processes. Zbl 0923.34005
Gorenflo, R.; Rutman, R.
21
1995
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
19
1997
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco
19
2004
Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082
Gorenflo, Rudolf; Mainardi, Francesco
18
2001
On the Cauchy and multi-point problems for partial pseudo-differential equations of fractional order. Zbl 1033.35160
Gorenflo, Rudolf; Luchko, Yurii F.; Umarov, Sabir R.
16
2000
Fully discrete random walks for space-time fractional diffusion equations. Zbl 1145.60312
Gorenflo, Rudolf; Vivoli, Alessandro
16
2003
Nonlinear two-term time fractional diffusion-wave problem. Zbl 1203.35289
Stojanović, Mirjana; Gorenflo, Rudolf
16
2010
Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
14
2007
Moment theory and some inverse problems in potential theory and heat conduction. Zbl 1005.30025
Ang, Dang Dinh; Gorenflo, Rudolf; Le, Vy Khoi; Trong, Dang Duc
14
2002
Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
13
2007
Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion. Zbl 1127.65100
Gorenflo, R.; Abdel-Rehim, E. A.
13
2007
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
12
2003
From power laws to fractional diffusion: the direct way. Zbl 1086.60049
Gorenflo, R.; Abdel-Rehim, Entsar A.
11
2004
Fractional relaxation of distributed order. Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
10
2006
A multi-dimensional Hausdorff moment problems regularization by finite moments. Zbl 0921.65089
Ang, D. D.; Gorenflo, R.; Trong, D. D.
10
1999
Asymptotics of singular values of fractional integral operators. Zbl 0808.45001
Vu Kim Tuan; Gorenflo, Rudolf
9
1994
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
8
2004
Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021
Gorenflo, R.; Mainardi, F.
8
1998
Discrete models of time-fractional diffusion in a potential well. Zbl 1129.26002
Gorenflo, R.; Abdel-Rehim, E. A.
8
2005
On multi-dimensional random walk models approximating symmetric space-fractional diffusion processes. Zbl 1131.60038
Umarov, Sabir; Gorenflo, Rudolf
8
2005
On solvability of linear fractional differential equations in Banach spaces. Zbl 1041.34045
Gorenflo, R.; Luchko, Yu. F.; Zabrejko, P. P.
8
1999
Simulation of the continuous time random walk of the space-fractional diffusion equations. Zbl 1153.65007
Abdel-Rehim, E. A.; Gorenflo, R.
8
2008
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
7
2015
On optimal regularization methods for fractional differentiation. Zbl 0941.65140
Tautenhahn, U.; Gorenflo, R.
7
1999
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
7
2012
Operational method for solving integral equations with Gauss’ hypergeometric function as a kernel. Zbl 0889.45005
Gorenflo, R.; Luchko, Yu. F.; Srivastava, H. M.
5
1997
Singular value decomposition of fractional integration operators in \(L_ 2\)-spaces with weights. Zbl 0824.45002
Gorenflo, R.; Vu Kim Tuan
5
1995
Asymptotics of singular values of Volterra integral operators. Zbl 0858.47021
Yu Kim Tuan; Gorenflo, Rudolf
5
1996
Solution of an Abel-type integral equation in the presence of noise by quadratic programming. Zbl 0196.51106
Gorenflo, R.; Kovetz, Y.
5
1966
Funktionentheoretische Bestimmung des Außenfeldes zu einer zweidimensionalen magnetohydrostatischen Konfiguration. Zbl 0127.16903
Gorenflo, R.
5
1965
Locally controllable regularization of Abel integral equations via operator complementation. Zbl 0898.65096
Gorenflo, Rudolf; Medvedeva, T.; Rubin, Boris
4
1997
Conservative difference schemes for diffusion problems with boundary and interface conditions. Zbl 0445.65091
Gorenflo, R.; Niedack, Marianne
4
1980
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
4
2004
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1411.60052
Gorenflo, R.; Vivoli, A.; Mainardi, F.
4
2006
Über S. Gerschgorins Methode der Fehlerabschätzung bei Differenzenverfahren. Zbl 0267.65073
Gorenflo, Rudolf
4
1973
On analysis and discretization of nonlinear Abel integral equations of first kind. Zbl 0883.65114
Gorenflo, Rudolf; Pfeiffer, Andreas
3
1991
Towards the Cauchy problem for the Laplace equation. Zbl 0820.35032
Dinh Nho Hào; Tran Duc Van; Gorenflo, Rudolf
3
1992
On asymptotic solutions of nonlinear Abel-Volterra integral equations with quasipolynomial free term. Zbl 0858.45007
Kilbas, Anatoly A.; Saigo, Megumi; Gorenflo, Rudolf
3
1995
Singular values of fractional and Volterra integral operators. Zbl 0829.45001
Vu Kim Tuan; Gorenflo, Rudolf
3
1995
Conservative difference schemes for diffusion problems. Zbl 0377.65047
Gorenflo, Rudolf
3
1978
Mellin convolution for subordinated stable processes. Zbl 1411.60026
Mainardi, F.; Pagnini, G.; Gorenflo, R.
3
2006
On some boundary value problems for pseudo-differential equations with boundary operators of fractional order. Zbl 1033.35162
Gorenflo, Rudolf; Luchko, Yurii F.; Umarov, Sabir R.
3
2000
Differenzenschemata monotoner Art für lineare parabolische Randwertaufgaben. Zbl 0244.35004
Gorenflo, R.
3
1971
A noncharacteristic Cauchy problem for the heat equation. Zbl 0741.35090
Dinh Nho Hào; Gorenflo, Rudolf
2
1991
On stabilizing the inversion of Abel integral operators. Zbl 0751.45002
Gorenflo, Rudolf
2
1990
Stochastic processes related to time-fractional diffusion-wave equation. Zbl 1329.60104
Gorenflo, Rudolf
2
2014
Regularization of a generalized Abel integral equation. Zbl 0726.65154
Dang Dinh Ang; Gorenflo, Rudolf; Dang Dinh Hai
2
1992
Inverse problems: principles and applications in geophysics, technology, and medicine. Proceedings of the international conference held in Potsdam, Germany, August 30-September 3, 1993. Zbl 0777.00024
2
1993
On the regularization of fractional differentiation of arbitrary positive order. Zbl 0810.65137
Vu Kim Tuan; Gorenflo, Rudolf
2
1994
The Grünwald-Letnikov difference operator and regularization of the Weyl fractional differentiation. Zbl 0804.65140
Vu Kim Tuan; Gorenflo, R.
2
1994
Locally controllable regularization of fractional derivatives. Zbl 0815.65142
Gorenflo, Rudolf; Rubin, Boris
2
1994
Asymptotic solution of a nonlinear Abel-Volterra integral equation of second kind. Zbl 0838.45004
Gorenflo, Rudolf; Kilbas, Anatoly A.
2
1995
On regularized inversion of Abel integral operators. Zbl 0852.65132
Gorenflo, Rudolf; Yamamoto, Masahiro
2
1995
On the dependence of asymptotics of \(S\)-numbers of fractional integration operators on weight functions. Zbl 0912.47011
Gorenflo, R.; Samko, S.
2
1997
Regularization of a two-dimensional inverse Stefan problem. Zbl 0837.35148
Gorenflo, R.; Ang, D. D.; Thanh, D. N.
2
1995
Differenzenschemata monotoner Art für schwach gekoppelte Systeme parabolischer Differentialgleichungen mit gemischten Randbedingungen. Zbl 0241.65070
Gorenflo, R.
2
1971
Differenzenschemata vom Irrfahrttypus für die Differentialgleichung von Fokker-Planck-Kolmogorov. Zbl 0258.65105
Gorenflo, R.
2
1968
On the autoconvolution equation and total variation constraints. Zbl 0923.65098
Fleischer, G.; Gorenflo, R.; Hofmann, B.
2
1999
Theory and practice of geophysical data inversion. Proceedings of the 8th international mathematical geophysics seminar on model optimization in exploration geophysics, held in Berlin, Germany, August 1990. Zbl 0754.73012
1
1992
A nonlinear Abel integral equation. Zbl 0770.45008
Ang, Dang Dinh; Gorenflo, Rudolf
1
1991
On the integral convolution for inverse \(G\)-transforms. Zbl 0885.44005
Gorenflo, Rudolf; Yakubovich, Semen B.
1
1994
Mittag-Leffler functions, related topics and applications. 2nd extended and updated edition. Zbl 1451.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
33
2020
Fractional differentiation of the product of Bessel functions of the first kind. Zbl 1332.26014
Sebastian, Nicy; Gorenflo, Rudolf
1
2016
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
88
2015
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
7
2015
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
462
2014
Hilfer-Prabhakar derivatives and some applications. Zbl 1334.26008
Garra, Roberto; Gorenflo, Rudolf; Polito, Federico; Tomovski, Živorad
83
2014
Stochastic processes related to time-fractional diffusion-wave equation. Zbl 1329.60104
Gorenflo, Rudolf
2
2014
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana
67
2013
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
7
2012
Nonlinear two-term time fractional diffusion-wave problem. Zbl 1203.35289
Stojanović, Mirjana; Gorenflo, Rudolf
16
2010
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
64
2009
Subordination in fractional diffusion processes via continuous time random walk. Zbl 1181.26015
Gorenflo, R.; Mainardi, F.; Vivoli, A.
1
2009
Time-fractional diffusion of distributed order. Zbl 1229.35118
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
76
2008
Simulation of the continuous time random walk of the space-fractional diffusion equations. Zbl 1153.65007
Abdel-Rehim, E. A.; Gorenflo, R.
8
2008
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
77
2007
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
51
2007
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
47
2007
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
43
2007
Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
14
2007
Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
13
2007
Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion. Zbl 1127.65100
Gorenflo, R.; Abdel-Rehim, E. A.
13
2007
Fractional relaxation of distributed order. Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
10
2006
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1411.60052
Gorenflo, R.; Vivoli, A.; Mainardi, F.
4
2006
Mellin convolution for subordinated stable processes. Zbl 1411.60026
Mainardi, F.; Pagnini, G.; Gorenflo, R.
3
2006
Fractional diffusion in inhomogeneous media. Zbl 1082.76097
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.
100
2005
Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations. I. Zbl 1100.35132
Umarov, Sabir; Gorenflo, Rudolf
36
2005
Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
21
2005
Discrete models of time-fractional diffusion in a potential well. Zbl 1129.26002
Gorenflo, R.; Abdel-Rehim, E. A.
8
2005
On multi-dimensional random walk models approximating symmetric space-fractional diffusion processes. Zbl 1131.60038
Umarov, Sabir; Gorenflo, Rudolf
8
2005
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
72
2004
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco
19
2004
From power laws to fractional diffusion: the direct way. Zbl 1086.60049
Gorenflo, R.; Abdel-Rehim, Entsar A.
11
2004
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
8
2004
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
4
2004
Distributed order time fractional diffusion equation. Zbl 1089.60046
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu.
89
2003
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
27
2003
Fully discrete random walks for space-time fractional diffusion equations. Zbl 1145.60312
Gorenflo, Rudolf; Vivoli, Alessandro
16
2003
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
12
2003
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
157
2002
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
114
2002
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
90
2002
Moment theory and some inverse problems in potential theory and heat conduction. Zbl 1005.30025
Ang, Dang Dinh; Gorenflo, Rudolf; Le, Vy Khoi; Trong, Dang Duc
14
2002
The tomato salad problem in spherical stereology. Zbl 1049.45003
Gorenflo, R.
1
2002
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
152
2001
Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082
Gorenflo, Rudolf; Mainardi, Francesco
18
2001
On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
173
2000
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
128
2000
Fractional calculus: Special functions and applications. Zbl 1030.26004
Mainardi, F.; Gorenflo, R.
73
2000
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
51
2000
On the Cauchy and multi-point problems for partial pseudo-differential equations of fractional order. Zbl 1033.35160
Gorenflo, Rudolf; Luchko, Yurii F.; Umarov, Sabir R.
16
2000
On some boundary value problems for pseudo-differential equations with boundary operators of fractional order. Zbl 1033.35162
Gorenflo, Rudolf; Luchko, Yurii F.; Umarov, Sabir R.
3
2000
An operational method for solving fractional differential equations with the Caputo derivatives. Zbl 0931.44003
Luchko, Yurii; Gorenflo, Rudolf
173
1999
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
119
1999
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
39
1999
Operator theoretic treatment of linear Abel integral equations of first kind. Zbl 1306.47057
Gorenflo, Rudolf; Yamamoto, Masahiro
25
1999
A multi-dimensional Hausdorff moment problems regularization by finite moments. Zbl 0921.65089
Ang, D. D.; Gorenflo, R.; Trong, D. D.
10
1999
On solvability of linear fractional differential equations in Banach spaces. Zbl 1041.34045
Gorenflo, R.; Luchko, Yu. F.; Zabrejko, P. P.
8
1999
On optimal regularization methods for fractional differentiation. Zbl 0941.65140
Tautenhahn, U.; Gorenflo, R.
7
1999
On the autoconvolution equation and total variation constraints. Zbl 0923.65098
Fleischer, G.; Gorenflo, R.; Hofmann, B.
2
1999
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
134
1998
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
54
1998
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
45
1998
On the generalized Mittag-Leffler type functions. Zbl 0935.33012
Gorenflo, R.; Kilbas, A. A.; Rogosin, S. V.
42
1998
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
35
1998
Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021
Gorenflo, R.; Mainardi, F.
8
1998
On the properties of a generalized function of Mittag-Leffler type. Zbl 1039.33503
Gorenflo, R.; Kilbas, A. A.; Rogozin, S. V.
1
1998
Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010
Gorenflo, R.; Mainardi, F.
132
1997
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
19
1997
Operational method for solving integral equations with Gauss’ hypergeometric function as a kernel. Zbl 0889.45005
Gorenflo, R.; Luchko, Yu. F.; Srivastava, H. M.
5
1997
Locally controllable regularization of Abel integral equations via operator complementation. Zbl 0898.65096
Gorenflo, Rudolf; Medvedeva, T.; Rubin, Boris
4
1997
On the dependence of asymptotics of \(S\)-numbers of fractional integration operators on weight functions. Zbl 0912.47011
Gorenflo, R.; Samko, S.
2
1997
Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
44
1996
Asymptotics of singular values of Volterra integral operators. Zbl 0858.47021
Yu Kim Tuan; Gorenflo, Rudolf
5
1996
Extrapolation to the limit for numerical fractional differentiation. Zbl 0860.65011
Vu Kim Tuan; Gorenflo, R.
21
1995
On ultraslow and intermediate processes. Zbl 0923.34005
Gorenflo, R.; Rutman, R.
21
1995
Singular value decomposition of fractional integration operators in \(L_ 2\)-spaces with weights. Zbl 0824.45002
Gorenflo, R.; Vu Kim Tuan
5
1995
On asymptotic solutions of nonlinear Abel-Volterra integral equations with quasipolynomial free term. Zbl 0858.45007
Kilbas, Anatoly A.; Saigo, Megumi; Gorenflo, Rudolf
3
1995
Singular values of fractional and Volterra integral operators. Zbl 0829.45001
Vu Kim Tuan; Gorenflo, Rudolf
3
1995
Asymptotic solution of a nonlinear Abel-Volterra integral equation of second kind. Zbl 0838.45004
Gorenflo, Rudolf; Kilbas, Anatoly A.
2
1995
On regularized inversion of Abel integral operators. Zbl 0852.65132
Gorenflo, Rudolf; Yamamoto, Masahiro
2
1995
Regularization of a two-dimensional inverse Stefan problem. Zbl 0837.35148
Gorenflo, R.; Ang, D. D.; Thanh, D. N.
2
1995
Existence of global quasiclassical solutions to the Cauchy problem for Hamilton-Jacobi equations. Zbl 0856.35021
Tran Duc Van; Nguyen Hoang; Gorenflo, R.
1
1995
Inverse problems and applications to geophysics, industry, medicine and technology. Proceedings of the international workshop on inverse problems, 17-19 January 1995, HoChiMinh City, Vietnam. Zbl 0810.00017
1
1995
On autoconvolution and regularization. Zbl 0804.45003
Gorenflo, Rudolf; Hofmann, Bernd
30
1994
Asymptotics of singular values of fractional integral operators. Zbl 0808.45001
Vu Kim Tuan; Gorenflo, Rudolf
9
1994
On the regularization of fractional differentiation of arbitrary positive order. Zbl 0810.65137
Vu Kim Tuan; Gorenflo, Rudolf
2
1994
The Grünwald-Letnikov difference operator and regularization of the Weyl fractional differentiation. Zbl 0804.65140
Vu Kim Tuan; Gorenflo, R.
2
1994
Locally controllable regularization of fractional derivatives. Zbl 0815.65142
Gorenflo, Rudolf; Rubin, Boris
2
1994
On the integral convolution for inverse \(G\)-transforms. Zbl 0885.44005
Gorenflo, Rudolf; Yakubovich, Semen B.
1
1994
On nondegenerate and degenerate nonlinear Abel integral equations of the first kind. Zbl 0796.45008
Dang Dinh Ang; Gorenflo, Rudolf
1
1994
On Abel type integral equations of first kind. Zbl 0807.45003
Gorenflo, Rudolf; Kilbas, Anatoly A.; Yakubovich, Semen B.
1
1994
Inverse problems: principles and applications in geophysics, technology, and medicine. Proceedings of the international conference held in Potsdam, Germany, August 30-September 3, 1993. Zbl 0777.00024
2
1993
A regularization method for the moment problem. Zbl 0789.65095
Ang, D. D.; Le, Vy Khoi; Gorenflo, R.
1
1993
Towards the Cauchy problem for the Laplace equation. Zbl 0820.35032
Dinh Nho Hào; Tran Duc Van; Gorenflo, Rudolf
3
1992
Regularization of a generalized Abel integral equation. Zbl 0726.65154
Dang Dinh Ang; Gorenflo, Rudolf; Dang Dinh Hai
2
1992
Theory and practice of geophysical data inversion. Proceedings of the 8th international mathematical geophysics seminar on model optimization in exploration geophysics, held in Berlin, Germany, August 1990. Zbl 0754.73012
1
1992
Abel integral equations. Analysis and applications. Zbl 0717.45002
Gorenflo, Rudolf; Vessella, Sergio
153
1991
On analysis and discretization of nonlinear Abel integral equations of first kind. Zbl 0883.65114
Gorenflo, Rudolf; Pfeiffer, Andreas
3
1991
A noncharacteristic Cauchy problem for the heat equation. Zbl 0741.35090
Dinh Nho Hào; Gorenflo, Rudolf
2
1991
A nonlinear Abel integral equation. Zbl 0770.45008
Ang, Dang Dinh; Gorenflo, Rudolf
1
1991
...and 21 more Documents
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Cited by 3,100 Authors

54 Liu, Fawang
48 Mainardi, Francesco
45 Băleanu, Dumitru I.
38 Gorenflo, Rudolf
30 Anh, Vo V.
30 Turner, Ian William
25 Povstenko, Yuriy Z.
24 Meerschaert, Mark Marvin
23 Tarasov, Vasily E.
23 Yamamoto, Masahiro
22 Chen, Yangquan
21 de Oliveira, Edmundo Capelas
21 Luchko, Yuri
20 Hofmann, Bernd
19 Beghin, Luisa
19 Leonenko, Nikolai N.
18 Garrappa, Roberto
18 Pagnini, Gianni
18 Sun, Zhizhong
18 Tomovski, Živorad
17 Srivastava, Hari Mohan
17 Wei, Ting
16 Ansari, Alireza
16 Daftardar-Gejji, Varsha
16 Polito, Federico
15 Abdeljawad, Thabet
15 Lizama, Carlos
15 Luchko, Yurii F.
15 Machado, José António Tenreiro
15 Sandev, Trifce
15 Wang, Hong
15 Wang, Jinrong
15 Warma, Mahamadi
14 Kiryakova, Virginia S.
13 Bulavatskyĭ, Volodymyr M.
13 Garra, Roberto
13 Jafari, Hossein
13 Odibat, Zaid M.
13 Saxena, Ram Kishore
13 Trujillo, Juan J.
12 Atanackovic, Teodor M.
12 Bhalekar, Sachin
12 Budak, Hüseyin
12 Fernandez, Arran
12 Sun, Hongguang
12 Tatar, Nasser-eddine
11 Agarwal, Praveen
11 Atangana, Abdon
11 Ford, Neville J.
11 Fu, Chuli
11 Jin, Bangti
11 Mathai, Arakaparampli Mathai
11 Nguyen Huy Tuan
11 Orsingher, Enzo
11 Scalas, Enrico
11 Sooppy Nisar, Kottakkaran
11 Xiong, Xiangtuan
11 Zheng, Xiangcheng
10 Ashurov, Ravshan Rajabovich
10 Chen, Wen
10 Farid, Ghulam
10 Ge, Fudong
10 Giusti, Andrea
10 Kaltenbacher, Barbara
10 Li, Changpin
10 Li, Zhiyuan
10 Malik, Salman A.
10 Rogosin, Sergei V.
10 Ruzhansky, Michael V.
10 Sun, Haiwei
9 Deng, Weihua
9 Górska, Katarzyna
9 Karniadakis, George Em
9 Mehrez, Khaled
9 Momani, Shaher M.
9 Roscani, Sabrina D.
9 Rundell, William
9 Sarikaya, Mehmet Zeki
9 Trong, Dang Duc
9 Vanterler da Costa Sousa, José
9 Vellaisamy, Palaniappan
9 Vieira, Nelson
9 Wang, Yuanming
9 Xu, Chuanju
9 Zhou, Zhi
8 Bazhlekova, Emilia G.
8 Burrage, Kevin
8 Chechkin, Aleksei V.
8 Diethelm, Kai
8 Duan, Junsheng
8 Fečkan, Michal
8 Ferreira, Milton
8 Horzela, Andrzej
8 Janno, Jaan
8 Keyantuo, Valentin
8 Lazarov, Raytcho D.
8 Macci, Claudio
8 Mahmudov, Nazim Idrisoglu
8 Stojanović, Mirjana N.
8 Tarasova, Valentina V.
...and 3,000 more Authors
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Cited in 427 Serials

188 Fractional Calculus & Applied Analysis
123 Applied Mathematics and Computation
97 Computers & Mathematics with Applications
89 Journal of Computational and Applied Mathematics
83 Advances in Difference Equations
64 Chaos, Solitons and Fractals
53 Journal of Computational Physics
51 Journal of Mathematical Analysis and Applications
49 Communications in Nonlinear Science and Numerical Simulation
41 Physica A
38 Computational and Applied Mathematics
38 Nonlinear Dynamics
38 Abstract and Applied Analysis
35 Applied Numerical Mathematics
33 Journal of Scientific Computing
33 Integral Transforms and Special Functions
29 Inverse Problems
29 Numerical Algorithms
28 Journal of Mathematical Physics
27 Journal of Applied Mathematics and Computing
23 International Journal of Computer Mathematics
23 Mathematical Problems in Engineering
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20 Mathematics and Computers in Simulation
20 Inverse Problems in Science and Engineering
19 Advances in Mathematical Physics
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19 International Journal of Applied and Computational Mathematics
17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
17 Journal of Function Spaces
16 Journal of Statistical Physics
16 AIMS Mathematics
15 Applied Mathematics Letters
15 Journal of Integral Equations and Applications
15 Stochastic Processes and their Applications
15 Fractals
15 Journal of Inverse and Ill-Posed Problems
15 Lobachevskii Journal of Mathematics
15 International Journal of Differential Equations
13 Zeitschrift für Analysis und ihre Anwendungen
13 Cybernetics and Systems Analysis
13 Filomat
13 Fractional Differential Calculus
12 Applicable Analysis
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12 Statistics & Probability Letters
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12 Journal of Inequalities and Applications
12 Discrete and Continuous Dynamical Systems. Series B
11 Mathematical Methods in the Applied Sciences
11 Journal of Differential Equations
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10 Mediterranean Journal of Mathematics
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9 Acta Mechanica
9 Reports on Mathematical Physics
9 Meccanica
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8 Journal of Mathematics
7 ZAMP. Zeitschrift für angewandte Mathematik und Physik
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7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
6 Mathematical Notes
6 Computing
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6 Semigroup Forum
6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
6 Journal of Vibration and Control
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6 Mathematical Modelling and Analysis
6 Journal of Evolution Equations
6 Computational Methods in Applied Mathematics
6 Axioms
6 Evolution Equations and Control Theory
5 Advances in Applied Probability
5 Integral Equations and Operator Theory
5 Ricerche di Matematica
5 Stochastic Analysis and Applications
5 Numerical Methods for Partial Differential Equations
5 Communications in Statistics. Theory and Methods
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