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Gorenflo, Rudolf

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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: IdRef · Google Scholar · MGP · Math-Net.Ru · Wikidata · dblp · GND
Documents Indexed: 153 Publications since 1961, including 10 Books
Reviewing Activity: 231 Reviews
Biographic References: 4 Publications
all top 5

Co-Authors

30 single-authored
40 Mainardi, Francesco
11 Ang, Dang Dinh
7 Luchko, Yuri
7 Tran Duc Van
7 Vivoli, Alessandro
7 Vu Kim Tuan
6 Kilbas, Anatoliĭ Aleksandrovich
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.
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 Vogel, Andreas
2 Yakubovich, Semyon B.
1 Anger, Gottfried
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 Kilbas, Anatoly A.
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-Hoang, Son
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

Publications by Year

Citations contained in zbMATH Open

120 Publications have been cited 3,211 times in 2,158 Documents Cited by Year
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
329
2014
On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
156
2000
Abel integral equations. Analysis and applications. Zbl 0717.45002
Gorenflo, Rudolf; Vessella, Sergio
145
1991
An operational method for solving fractional differential equations with the Caputo derivatives. Zbl 0931.44003
Luchko, Yurii; Gorenflo, Rudolf
142
1999
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
137
2002
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
129
2001
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
121
2000
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
117
1998
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
Distributed order time fractional diffusion equation. Zbl 1089.60046
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu.
81
2003
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
78
2002
Fractional diffusion in inhomogeneous media. Zbl 1082.76097
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.
74
2005
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
73
2015
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
68
2004
Time-fractional diffusion of distributed order. Zbl 1229.35118
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
67
2008
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
61
2007
Hilfer-Prabhakar derivatives and some applications. Zbl 1334.26008
Garra, Roberto; Gorenflo, Rudolf; Polito, Federico; Tomovski, Živorad
58
2014
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
58
2009
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 calculus: integral and differential equations of fractional order. Zbl 1438.26010
Gorenflo, R.; Mainardi, F.
49
1997
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
46
2007
Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161
Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri
44
2000
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
43
1998
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
42
1998
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
42
2007
Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
41
1996
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
38
1999
On the generalized Mittag-Leffler type functions. Zbl 0935.33012
Gorenflo, R.; Kilbas, A. A.; Rogosin, S. V.
34
1998
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
34
2007
Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations. I. Zbl 1100.35132
Umarov, Sabir; Gorenflo, Rudolf
31
2005
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
28
1998
On autoconvolution and regularization. Zbl 0804.45003
Gorenflo, Rudolf; Hofmann, Bernd
28
1994
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
24
2003
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.
20
1995
Operator theoretic treatment of linear Abel integral equations of first kind. Zbl 1306.47057
Gorenflo, Rudolf; Yamamoto, Masahiro
19
1999
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco
18
2004
Extrapolation to the limit for numerical fractional differentiation. Zbl 0860.65011
Vu Kim Tuan; Gorenflo, R.
17
1995
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
Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082
Gorenflo, Rudolf; Mainardi, Francesco
15
2001
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
13
2002
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
13
1997
Nonlinear two-term time fractional diffusion-wave problem. Zbl 1203.35289
Stojanović, Mirjana; Gorenflo, Rudolf
13
2010
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.
11
2007
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.
11
2020
A multi-dimensional Hausdorff moment problems regularization by finite moments. Zbl 0921.65089
Ang, D. D.; Gorenflo, R.; Trong, D. D.
10
1999
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
10
2003
From power laws to fractional diffusion: the direct way. Zbl 1086.60049
Gorenflo, R.; Abdel-Rehim, Entsar A.
10
2004
Fractional relaxation of distributed order. Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
9
2006
Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021
Gorenflo, R.; Mainardi, F.
8
1998
On solvability of linear fractional differential equations in Banach spaces. Zbl 1041.34045
Gorenflo, R.; Luchko, Yu. F.; Zabrejko, P. P.
8
1999
Discrete models of time-fractional diffusion in a potential well. Zbl 1129.26002
Gorenflo, R.; Abdel-Rehim, E. A.
8
2005
On optimal regularization methods for fractional differentiation. Zbl 0941.65140
Tautenhahn, U.; Gorenflo, R.
7
1999
Asymptotics of singular values of fractional integral operators. Zbl 0808.45001
Vu Kim Tuan; Gorenflo, Rudolf
7
1994
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
7
2004
On multi-dimensional random walk models approximating symmetric space-fractional diffusion processes. Zbl 1131.60038
Umarov, Sabir; Gorenflo, Rudolf
7
2005
Simulation of the continuous time random walk of the space-fractional diffusion equations. Zbl 1153.65007
Abdel-Rehim, E. A.; Gorenflo, R.
6
2008
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
5
2012
Singular value decomposition of fractional integration operators in \(L_ 2\)-spaces with weights. Zbl 0824.45002
Gorenflo, R.; Vu Kim Tuan
5
1995
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
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1411.60052
Gorenflo, R.; Vivoli, A.; Mainardi, F.
4
2006
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
4
2004
Asymptotics of singular values of Volterra integral operators. Zbl 0858.47021
Yu Kim Tuan; Gorenflo, Rudolf
4
1996
Operational method for solving integral equations with Gauss’ hypergeometric function as a kernel. Zbl 0889.45005
Gorenflo, R.; Luchko, Yu. F.; Srivastava, H. M.
4
1997
Locally controllable regularization of Abel integral equations via operator complementation. Zbl 0898.65096
Gorenflo, Rudolf; Medvedeva, T.; Rubin, Boris
4
1997
Über S. Gerschgorins Methode der Fehlerabschätzung bei Differenzenverfahren. Zbl 0267.65073
Gorenflo, Rudolf
4
1973
Conservative difference schemes for diffusion problems with boundary and interface conditions. Zbl 0445.65091
Gorenflo, R.; Niedack, Marianne
4
1980
Mellin convolution for subordinated stable processes. Zbl 1411.60026
Mainardi, F.; Pagnini, G.; Gorenflo, R.
3
2006
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
Towards the Cauchy problem for the Laplace equation. Zbl 0820.35032
Dinh Nho Hào; Tran Duc Van; Gorenflo, Rudolf
3
1992
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
On analysis and discretization of nonlinear Abel integral equations of first kind. Zbl 0883.65114
Gorenflo, Rudolf; Pfeiffer, Andreas
3
1991
Differenzenschemata monotoner Art für lineare parabolische Randwertaufgaben. Zbl 0244.35004
Gorenflo, R.
3
1971
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
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
3
2015
Stochastic processes related to time-fractional diffusion-wave equation. Zbl 1329.60104
Gorenflo, Rudolf
2
2014
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 autoconvolution equation and total variation constraints. Zbl 0923.65098
Fleischer, G.; Gorenflo, R.; Hofmann, B.
2
1999
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
Anger, Gottfried (ed.); Gorenflo, Rudolf (ed.); Jochmann, Horst (ed.); Moritz, Helmut (ed.); Webers, Wigor (ed.)
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
On the dependence of asymptotics of \(S\)-numbers of fractional integration operators on weight functions. Zbl 0912.47011
Gorenflo, R.; Samko, S.
2
1997
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
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
Regularization of a two-dimensional inverse Stefan problem. Zbl 0837.35148
Gorenflo, R.; Ang, D. D.; Thanh, D. N.
2
1995
Regularization of a generalized Abel integral equation. Zbl 0726.65154
Dang Dinh Ang; Gorenflo, Rudolf; Dang Dinh Hai
2
1992
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
A regularization method for the moment problem. Zbl 0789.65095
Ang, D. D.; Le, Vy Khoi; Gorenflo, R.
1
1993
On nondegenerate and degenerate nonlinear Abel integral equations of the first kind. Zbl 0796.45008
Dang Dinh Ang; Gorenflo, Rudolf
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.
11
2020
Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513
Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro
73
2015
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
3
2015
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
329
2014
Hilfer-Prabhakar derivatives and some applications. Zbl 1334.26008
Garra, Roberto; Gorenflo, Rudolf; Polito, Federico; Tomovski, Živorad
58
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
57
2013
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
5
2012
Nonlinear two-term time fractional diffusion-wave problem. Zbl 1203.35289
Stojanović, Mirjana; Gorenflo, Rudolf
13
2010
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
58
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
67
2008
Simulation of the continuous time random walk of the space-fractional diffusion equations. Zbl 1153.65007
Abdel-Rehim, E. A.; Gorenflo, R.
6
2008
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
61
2007
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
46
2007
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
42
2007
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
34
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.
11
2007
Fractional relaxation of distributed order. Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
9
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.
74
2005
Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations. I. Zbl 1100.35132
Umarov, Sabir; Gorenflo, Rudolf
31
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
7
2005
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
68
2004
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco
18
2004
From power laws to fractional diffusion: the direct way. Zbl 1086.60049
Gorenflo, R.; Abdel-Rehim, Entsar A.
10
2004
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
7
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.
81
2003
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
24
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
10
2003
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
137
2002
Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016
Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri
104
2002
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
78
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
13
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
129
2001
Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082
Gorenflo, Rudolf; Mainardi, Francesco
15
2001
On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
156
2000
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
121
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
44
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
142
1999
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
104
1999
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
38
1999
Operator theoretic treatment of linear Abel integral equations of first kind. Zbl 1306.47057
Gorenflo, Rudolf; Yamamoto, Masahiro
19
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.
117
1998
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
43
1998
Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001
Luchko, Yu.; Gorenflo, R.
42
1998
On the generalized Mittag-Leffler type functions. Zbl 0935.33012
Gorenflo, R.; Kilbas, A. A.; Rogosin, S. V.
34
1998
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
28
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.
49
1997
Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003
Gorenflo, Rudolf; Luchko, Yuri
13
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.
4
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.
41
1996
Asymptotics of singular values of Volterra integral operators. Zbl 0858.47021
Yu Kim Tuan; Gorenflo, Rudolf
4
1996
On ultraslow and intermediate processes. Zbl 0923.34005
Gorenflo, R.; Rutman, R.
20
1995
Extrapolation to the limit for numerical fractional differentiation. Zbl 0860.65011
Vu Kim Tuan; Gorenflo, R.
17
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
Dang Dinh Ang; Gorenflo, R.; Rutman, R. S.; Tran Duc Van; Yamamoto, M.
1
1995
On autoconvolution and regularization. Zbl 0804.45003
Gorenflo, Rudolf; Hofmann, Bernd
28
1994
Asymptotics of singular values of fractional integral operators. Zbl 0808.45001
Vu Kim Tuan; Gorenflo, Rudolf
7
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 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
On the integral convolution for inverse \(G\)-transforms. Zbl 0885.44005
Gorenflo, Rudolf; 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
Anger, Gottfried; Gorenflo, Rudolf; Jochmann, Horst; Moritz, Helmut; Webers, Wigor
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
Vogel, Andreas; Sarwar, Abu K. M.; Gorenflo, Rudolf; Kounchev, Ognyan I.
1
1992
Abel integral equations. Analysis and applications. Zbl 0717.45002
Gorenflo, Rudolf; Vessella, Sergio
145
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
On Sobolev-Orlicz spaces of infinite order for a full Euclidean space. Zbl 0727.46019
Tran Duc Van; Ha Huy Bang; Gorenflo, R.
1
1991
A nonlinear Abel integral equation. Zbl 0770.45008
Ang, Dang Dinh; Gorenflo, Rudolf
1
1991
...and 20 more Documents
all top 5

Cited by 2,538 Authors

53 Liu, Fawang
47 Mainardi, Francesco
38 Gorenflo, Rudolf
34 Băleanu, Dumitru I.
30 Anh, Vo V.
30 Turner, Ian William
25 Povstenko, Yuriy Z.
23 Meerschaert, Mark Marvin
21 Chen, Yangquan
21 Luchko, Yuri
21 Yamamoto, Masahiro
19 Hofmann, Bernd
19 Tarasov, Vasily E.
18 Garrappa, Roberto
17 Beghin, Luisa
17 de Oliveira, Edmundo Capelas
17 Pagnini, Gianni
17 Sun, Zhizhong
16 Daftardar-Gejji, Varsha
16 Leonenko, Nikolai N.
16 Machado, José António Tenreiro
16 Tomovski, Živorad
15 Luchko, Yurii F.
15 Polito, Federico
15 Wang, Jinrong
15 Warma, Mahamadi
15 Wei, Ting
14 Kiryakova, Virginia S.
14 Lizama, Carlos
13 Ansari, Alireza
13 Jafari, Hossein
13 Odibat, Zaid M.
13 Sandev, Trifce
13 Saxena, Ram Kishore
13 Srivastava, Hari Mohan
13 Trujillo, Juan J.
12 Bhalekar, Sachin
12 Bulavatskyĭ, Volodymyr M.
12 Garra, Roberto
11 Atanackovic, Teodor M.
11 Fu, Chuli
11 Jin, Bangti
11 Mathai, Arakaparampli Mathai
11 Orsingher, Enzo
11 Sun, Hongguang
11 Wang, Hong
10 Ford, Neville J.
10 Ge, Fudong
10 Giusti, Andrea
10 Li, Zhiyuan
10 Nguyen Huy Tuan
10 Rogosin, Sergei V.
10 Scalas, Enrico
9 Atangana, Abdon
9 Chen, Wen
9 Li, Changpin
9 Momani, Shaher M.
9 Trong, Dang Duc
9 Wang, Yuanming
9 Xiong, Xiangtuan
9 Zhou, Zhi
8 Bazhlekova, Emilia G.
8 Burrage, Kevin
8 Deng, Weihua
8 Duan, Junsheng
8 Keyantuo, Valentin
8 Lazarov, Raytcho D.
8 Roscani, Sabrina D.
8 Rundell, William
8 Stojanović, Mirjana N.
8 Tarasova, Valentina V.
8 Umarov, Sabir R.
8 Vanterler da Costa Sousa, José
8 Vellaisamy, Palaniappan
8 Vieira, Nelson
8 Xu, Chuanju
8 Xu, Mingyu
8 Zaky, Mahmoud A.
8 Zheng, Xiangcheng
7 Abbaszadeh, Mostafa
7 Agarwal, Praveen
7 Avazzadeh, Zakieh
7 Chechkin, Aleksei V.
7 Chen, Changming
7 Dehghan Takht Fooladi, Mehdi
7 Diethelm, Kai
7 Ding, Hengfei
7 Fečkan, Michal
7 Ferreira, Milton
7 Hon, Yiu-Chung
7 Janno, Jaan
7 Karniadakis, George Em
7 Kilbas, Anatoliĭ Aleksandrovich
7 Kiliçman, Adem
7 Li, Lei
7 Liu, Jianguo
7 Nane, Erkan
7 Popolizio, Marina
7 Zhao, Zhenyu
7 Zheng, Guanghui
...and 2,438 more Authors
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Cited in 373 Serials

175 Fractional Calculus & Applied Analysis
110 Applied Mathematics and Computation
95 Computers & Mathematics with Applications
82 Journal of Computational and Applied Mathematics
50 Journal of Computational Physics
49 Journal of Mathematical Analysis and Applications
45 Advances in Difference Equations
42 Chaos, Solitons and Fractals
42 Communications in Nonlinear Science and Numerical Simulation
38 Nonlinear Dynamics
37 Abstract and Applied Analysis
33 Applied Numerical Mathematics
29 Integral Transforms and Special Functions
28 Journal of Mathematical Physics
28 Journal of Scientific Computing
27 Inverse Problems
26 Numerical Algorithms
26 Computational and Applied Mathematics
24 Journal of Applied Mathematics and Computing
23 Mathematical Problems in Engineering
21 Applied Mathematical Modelling
19 Mathematics
18 Inverse Problems in Science and Engineering
16 Journal of Statistical Physics
16 Physica A
16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
16 Advances in Mathematical Physics
15 Journal of Integral Equations and Applications
14 Applied Mathematics Letters
14 Journal of Inverse and Ill-Posed Problems
14 International Journal of Differential Equations
13 Zeitschrift für Analysis und ihre Anwendungen
13 International Journal of Applied and Computational Mathematics
12 Applicable Analysis
12 Numerical Functional Analysis and Optimization
12 Stochastic Processes and their Applications
12 Cybernetics and Systems Analysis
12 Engineering Analysis with Boundary Elements
11 Mathematical Methods in the Applied Sciences
11 Advances in Computational Mathematics
10 Journal of Differential Equations
10 Mathematics and Computers in Simulation
10 Chaos
10 Mediterranean Journal of Mathematics
10 Mathematical Modelling of Natural Phenomena
10 Journal of Function Spaces
9 Meccanica
9 SIAM Journal on Scientific Computing
9 Nonlinear Analysis. Real World Applications
9 Discrete and Continuous Dynamical Systems. Series B
9 Fractional Differential Calculus
8 Acta Mechanica
8 Journal of Applied Probability
8 Journal of Functional Analysis
8 Statistics & Probability Letters
8 International Journal of Computer Mathematics
8 Lobachevskii Journal of Mathematics
8 Journal of Applied Mathematics
7 Computer Methods in Applied Mechanics and Engineering
7 Proceedings of the American Mathematical Society
7 SIAM Journal on Numerical Analysis
7 Journal of Mathematics
6 Reports on Mathematical Physics
6 ZAMP. Zeitschrift für angewandte Mathematik und Physik
6 Computing
6 Numerische Mathematik
6 Journal of Vibration and Control
6 Differential Equations and Dynamical Systems
6 International Journal of Nonlinear Sciences and Numerical Simulation
6 Boundary Value Problems
6 Axioms
5 Advances in Applied Probability
5 Mathematics of Computation
5 Integral Equations and Operator Theory
5 Ricerche di Matematica
5 Semigroup Forum
5 Numerical Methods for Partial Differential Equations
5 SIAM Journal on Applied Mathematics
5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
5 Fractals
5 Complexity
5 Journal of Inequalities and Applications
5 Methodology and Computing in Applied Probability
5 Journal of Evolution Equations
5 Computational Methods in Applied Mathematics
5 Journal of Physics A: Mathematical and Theoretical
5 Inverse Problems and Imaging
5 Asian-European Journal of Mathematics
5 Journal of Nonlinear Science and Applications
5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
5 East Asian Journal on Applied Mathematics
4 International Journal of Modern Physics B
4 International Journal of Engineering Science
4 Physics Letters. A
4 BIT
4 Calcolo
4 Quarterly of Applied Mathematics
4 Mathematical and Computer Modelling
4 Signal Processing
4 Linear Algebra and its Applications
...and 273 more Serials
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Cited in 53 Fields

969 Partial differential equations (35-XX)
740 Numerical analysis (65-XX)
682 Real functions (26-XX)
454 Ordinary differential equations (34-XX)
304 Special functions (33-XX)
296 Probability theory and stochastic processes (60-XX)
280 Integral equations (45-XX)
158 Operator theory (47-XX)
104 Integral transforms, operational calculus (44-XX)
87 Fluid mechanics (76-XX)
83 Mechanics of deformable solids (74-XX)
81 Statistical mechanics, structure of matter (82-XX)
72 Systems theory; control (93-XX)
58 Biology and other natural sciences (92-XX)
55 Classical thermodynamics, heat transfer (80-XX)
39 Functions of a complex variable (30-XX)
39 Dynamical systems and ergodic theory (37-XX)
38 Statistics (62-XX)
38 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
34 Harmonic analysis on Euclidean spaces (42-XX)
34 Calculus of variations and optimal control; optimization (49-XX)
29 Approximations and expansions (41-XX)
28 Quantum theory (81-XX)
26 Functional analysis (46-XX)
19 Information and communication theory, circuits (94-XX)
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15 Optics, electromagnetic theory (78-XX)
13 Measure and integration (28-XX)
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