Edit Profile (opens in new tab) Gorenflo, Rudolf Compute Distance To: Compute Author ID: gorenflo.rudolf Published as: Gorenflo, Rudolf; Gorenflo, R.; Gorenfloh, Rudolf more...less 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: 232 Reviews Biographic References: 4 Publications Co-Authors: 80 Co-Authors with 122 Joint Publications 2,172 Co-Co-Authors all top 5 Co-Authors 30 single-authored 38 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 all top 5 Fields 64 Integral equations (45-XX) 53 Real functions (26-XX) 46 Numerical analysis (65-XX) 34 Partial differential equations (35-XX) 34 Probability theory and stochastic processes (60-XX) 27 Special functions (33-XX) 18 Integral transforms, operational calculus (44-XX) 12 Operator theory (47-XX) 8 Fluid mechanics (76-XX) 7 General and overarching topics; collections (00-XX) 6 Geophysics (86-XX) 5 Functions of a complex variable (30-XX) 5 Ordinary differential equations (34-XX) 5 Mechanics of deformable solids (74-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Mechanics of particles and systems (70-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 121 Publications have been cited 3,771 times in 2,599 Documents Cited by ▼ Year ▼ Mittag-Leffler functions, related topics and applications. Zbl 1309.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 456 2014 On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005Mainardi, Francesco; Gorenflo, Rudolf 172 2000 An operational method for solving fractional differential equations with the Caputo derivatives. Zbl 0931.44003Luchko, Yurii; Gorenflo, Rudolf 172 1999 Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo 153 2002 Abel integral equations. Analysis and applications. Zbl 0717.45002Gorenflo, Rudolf; Vessella, Sergio 151 1991 Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco 150 2001 Random walk models for space-fractional diffusion processes. Zbl 0946.60039Gorenflo, R.; Mainardi, F. 133 1998 Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 126 2000 Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010Gorenflo, R.; Mainardi, F. 118 1997 Analytical properties and applications of the Wright function. Zbl 1027.33006Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 116 1999 Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri 113 2002 Fractional diffusion in inhomogeneous media. Zbl 1082.76097Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M. 99 2005 Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo 88 2002 Distributed order time fractional diffusion equation. Zbl 1089.60046Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu. 87 2003 Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro 86 2015 Hilfer-Prabhakar derivatives and some applications. Zbl 1334.26008Garra, Roberto; Gorenflo, Rudolf; Polito, Federico; Tomovski, Živorad 80 2014 Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 75 2007 Time-fractional diffusion of distributed order. Zbl 1229.35118Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 75 2008 A fractional generalization of the Poisson processes. Zbl 1087.60064Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 72 2004 Fractional calculus: Special functions and applications. Zbl 1030.26004Mainardi, F.; Gorenflo, R. 72 2000 Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana 66 2013 Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004Gorenflo, Rudolf; Mainardi, Francesco 64 2009 Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001Luchko, Yu.; Gorenflo, R. 51 1998 Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri 51 2000 Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro 50 2007 Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304Mainardi, Francesco; Gorenflo, Rudolf 46 2007 Fractional calculus and stable probability distributions. Zbl 0934.35008Gorenflo, R.; Mainardi, F. 44 1998 Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011Gorenflo, R.; Mainardi, F. 43 1996 On the generalized Mittag-Leffler type functions. Zbl 0935.33012Gorenflo, R.; Kilbas, A. A.; Rogosin, S. V. 42 1998 The two forms of fractional relaxation of distributed order. Zbl 1165.26302Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana 41 2007 Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006Gorenflo, R.; Mainardi, F. 38 1999 Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations. I. Zbl 1100.35132Umarov, Sabir; Gorenflo, Rudolf 36 2005 Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M. 34 1998 On autoconvolution and regularization. Zbl 0804.45003Gorenflo, Rudolf; Hofmann, Bernd 30 1994 Mittag-Leffler functions, related topics and applications. 2nd extended and updated edition. Zbl 1451.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 29 2020 Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 27 2003 Operator theoretic treatment of linear Abel integral equations of first kind. Zbl 1306.47057Gorenflo, Rudolf; Yamamoto, Masahiro 25 1999 Extrapolation to the limit for numerical fractional differentiation. Zbl 0860.65011Vu Kim Tuan; Gorenflo, R. 21 1995 On ultraslow and intermediate processes. Zbl 0923.34005Gorenflo, R.; Rutman, R. 21 1995 Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 21 2005 Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco 19 2004 Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003Gorenflo, Rudolf; Luchko, Yuri 18 1997 Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082Gorenflo, Rudolf; Mainardi, Francesco 17 2001 On the Cauchy and multi-point problems for partial pseudo-differential equations of fractional order. Zbl 1033.35160Gorenflo, Rudolf; Luchko, Yurii F.; Umarov, Sabir R. 16 2000 Nonlinear two-term time fractional diffusion-wave problem. Zbl 1203.35289Stojanović, Mirjana; Gorenflo, Rudolf 16 2010 Fully discrete random walks for space-time fractional diffusion equations. Zbl 1145.60312Gorenflo, Rudolf; Vivoli, Alessandro 16 2003 Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 14 2007 Moment theory and some inverse problems in potential theory and heat conduction. Zbl 1005.30025Ang, Dang Dinh; Gorenflo, Rudolf; Le, Vy Khoi; Trong, Dang Duc 14 2002 Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 13 2007 Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion. Zbl 1127.65100Gorenflo, R.; Abdel-Rehim, E. A. 13 2007 Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco 12 2003 From power laws to fractional diffusion: the direct way. Zbl 1086.60049Gorenflo, R.; Abdel-Rehim, Entsar A. 10 2004 A multi-dimensional Hausdorff moment problems regularization by finite moments. Zbl 0921.65089Ang, D. D.; Gorenflo, R.; Trong, D. D. 10 1999 Fractional relaxation of distributed order. Zbl 1167.26303Gorenflo, Rudolf; Mainardi, Francesco 10 2006 Asymptotics of singular values of fractional integral operators. Zbl 0808.45001Vu Kim Tuan; Gorenflo, Rudolf 9 1994 Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021Gorenflo, R.; Mainardi, F. 8 1998 On solvability of linear fractional differential equations in Banach spaces. Zbl 1041.34045Gorenflo, R.; Luchko, Yu. F.; Zabrejko, P. P. 8 1999 Discrete models of time-fractional diffusion in a potential well. Zbl 1129.26002Gorenflo, R.; Abdel-Rehim, E. A. 8 2005 On multi-dimensional random walk models approximating symmetric space-fractional diffusion processes. Zbl 1131.60038Umarov, Sabir; Gorenflo, Rudolf 8 2005 Anomalous waiting times in high-frequency financial data. Zbl 1409.62216Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco 8 2004 Parametric subordination in fractional diffusion processes. Zbl 1371.60135Gorenflo, Rudolf; Mainardi, Francesco 7 2012 Simulation of the continuous time random walk of the space-fractional diffusion equations. Zbl 1153.65007Abdel-Rehim, E. A.; Gorenflo, R. 7 2008 On optimal regularization methods for fractional differentiation. Zbl 0941.65140Tautenhahn, U.; Gorenflo, R. 7 1999 On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051Gorenflo, Rudolf; Mainardi, Francesco 6 2015 Operational method for solving integral equations with Gauss’ hypergeometric function as a kernel. Zbl 0889.45005Gorenflo, R.; Luchko, Yu. F.; Srivastava, H. M. 5 1997 Singular value decomposition of fractional integration operators in \(L_ 2\)-spaces with weights. Zbl 0824.45002Gorenflo, R.; Vu Kim Tuan 5 1995 Funktionentheoretische Bestimmung des Außenfeldes zu einer zweidimensionalen magnetohydrostatischen Konfiguration. Zbl 0127.16903Gorenflo, R. 5 1965 Solution of an Abel-type integral equation in the presence of noise by quadratic programming. Zbl 0196.51106Gorenflo, R.; Kovetz, Y. 5 1966 Asymptotics of singular values of Volterra integral operators. Zbl 0858.47021Yu Kim Tuan; Gorenflo, Rudolf 5 1996 Über S. Gerschgorins Methode der Fehlerabschätzung bei Differenzenverfahren. Zbl 0267.65073Gorenflo, Rudolf 4 1973 Conservative difference schemes for diffusion problems with boundary and interface conditions. Zbl 0445.65091Gorenflo, R.; Niedack, Marianne 4 1980 A renewal process of Mittag-Leffler type. Zbl 1191.60101Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 4 2004 Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1411.60052Gorenflo, R.; Vivoli, A.; Mainardi, F. 4 2006 Locally controllable regularization of Abel integral equations via operator complementation. Zbl 0898.65096Gorenflo, Rudolf; Medvedeva, T.; Rubin, Boris 4 1997 Conservative difference schemes for diffusion problems. Zbl 0377.65047Gorenflo, Rudolf 3 1978 Towards the Cauchy problem for the Laplace equation. Zbl 0820.35032Dinh Nho Hào; Tran Duc Van; Gorenflo, Rudolf 3 1992 On analysis and discretization of nonlinear Abel integral equations of first kind. Zbl 0883.65114Gorenflo, Rudolf; Pfeiffer, Andreas 3 1991 Singular values of fractional and Volterra integral operators. Zbl 0829.45001Vu Kim Tuan; Gorenflo, Rudolf 3 1995 On asymptotic solutions of nonlinear Abel-Volterra integral equations with quasipolynomial free term. Zbl 0858.45007Kilbas, Anatoly A.; Saigo, Megumi; Gorenflo, Rudolf 3 1995 Differenzenschemata monotoner Art für lineare parabolische Randwertaufgaben. Zbl 0244.35004Gorenflo, R. 3 1971 On some boundary value problems for pseudo-differential equations with boundary operators of fractional order. Zbl 1033.35162Gorenflo, Rudolf; Luchko, Yurii F.; Umarov, Sabir R. 3 2000 Mellin convolution for subordinated stable processes. Zbl 1411.60026Mainardi, F.; Pagnini, G.; Gorenflo, R. 3 2006 Differenzenschemata vom Irrfahrttypus für die Differentialgleichung von Fokker-Planck-Kolmogorov. Zbl 0258.65105Gorenflo, R. 2 1968 Regularization of a generalized Abel integral equation. Zbl 0726.65154Dang Dinh Ang; Gorenflo, Rudolf; Dang Dinh Hai 2 1992 A noncharacteristic Cauchy problem for the heat equation. Zbl 0741.35090Dinh Nho Hào; Gorenflo, Rudolf 2 1991 On stabilizing the inversion of Abel integral operators. Zbl 0751.45002Gorenflo, Rudolf 2 1990 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 0810.65137Vu Kim Tuan; Gorenflo, Rudolf 2 1994 The Grünwald-Letnikov difference operator and regularization of the Weyl fractional differentiation. Zbl 0804.65140Vu Kim Tuan; Gorenflo, R. 2 1994 Locally controllable regularization of fractional derivatives. Zbl 0815.65142Gorenflo, Rudolf; Rubin, Boris 2 1994 Regularization of a two-dimensional inverse Stefan problem. Zbl 0837.35148Gorenflo, R.; Ang, D. D.; Thanh, D. N. 2 1995 Asymptotic solution of a nonlinear Abel-Volterra integral equation of second kind. Zbl 0838.45004Gorenflo, Rudolf; Kilbas, Anatoly A. 2 1995 On regularized inversion of Abel integral operators. Zbl 0852.65132Gorenflo, Rudolf; Yamamoto, Masahiro 2 1995 On the autoconvolution equation and total variation constraints. Zbl 0923.65098Fleischer, G.; Gorenflo, R.; Hofmann, B. 2 1999 Differenzenschemata monotoner Art für schwach gekoppelte Systeme parabolischer Differentialgleichungen mit gemischten Randbedingungen. Zbl 0241.65070Gorenflo, R. 2 1971 On the dependence of asymptotics of \(S\)-numbers of fractional integration operators on weight functions. Zbl 0912.47011Gorenflo, R.; Samko, S. 2 1997 Stochastic processes related to time-fractional diffusion-wave equation. Zbl 1329.60104Gorenflo, Rudolf 2 2014 Sobolev-Orlicz spaces of infinite order and nonlinear differential equations. Zbl 0711.35153Tran Duc Van; Gorenflo, R.; Le Van Hap 1 1990 On Sobolev-Orlicz spaces of infinite order for a full Euclidean space. Zbl 0727.46019Tran Duc Van; Ha Huy Bang; Gorenflo, R. 1 1991 Numerische Simulation von Diffusionsprozessen mit nichtnegativitätserhaltenden konservativen Differenzenverfahren. (Numerical simulation of diffusion processes with conservative difference schemes of non-negative type). Zbl 0582.65070Gorenflo, Rudolf; Kuban, Angelika 1 1982 Mittag-Leffler functions, related topics and applications. 2nd extended and updated edition. Zbl 1451.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 29 2020 Fractional differentiation of the product of Bessel functions of the first kind. Zbl 1332.26014Sebastian, Nicy; Gorenflo, Rudolf 1 2016 Time-fractional diffusion equation in the fractional Sobolev spaces. Zbl 06441513Gorenflo, Rudolf; Luchko, Yuri; Yamamoto, Masahiro 86 2015 On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051Gorenflo, Rudolf; Mainardi, Francesco 6 2015 Mittag-Leffler functions, related topics and applications. Zbl 1309.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 456 2014 Hilfer-Prabhakar derivatives and some applications. Zbl 1334.26008Garra, Roberto; Gorenflo, Rudolf; Polito, Federico; Tomovski, Živorad 80 2014 Stochastic processes related to time-fractional diffusion-wave equation. Zbl 1329.60104Gorenflo, Rudolf 2 2014 Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. Zbl 1312.35179Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana 66 2013 Parametric subordination in fractional diffusion processes. Zbl 1371.60135Gorenflo, Rudolf; Mainardi, Francesco 7 2012 Nonlinear two-term time fractional diffusion-wave problem. Zbl 1203.35289Stojanović, Mirjana; Gorenflo, Rudolf 16 2010 Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004Gorenflo, Rudolf; Mainardi, Francesco 64 2009 Subordination in fractional diffusion processes via continuous time random walk. Zbl 1181.26015Gorenflo, R.; Mainardi, F.; Vivoli, A. 1 2009 Time-fractional diffusion of distributed order. Zbl 1229.35118Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 75 2008 Simulation of the continuous time random walk of the space-fractional diffusion equations. Zbl 1153.65007Abdel-Rehim, E. A.; Gorenflo, R. 7 2008 Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 75 2007 Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro 50 2007 Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304Mainardi, Francesco; Gorenflo, Rudolf 46 2007 The two forms of fractional relaxation of distributed order. Zbl 1165.26302Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana 41 2007 Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 14 2007 Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 13 2007 Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion. Zbl 1127.65100Gorenflo, R.; Abdel-Rehim, E. A. 13 2007 Fractional relaxation of distributed order. Zbl 1167.26303Gorenflo, Rudolf; Mainardi, Francesco 10 2006 Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1411.60052Gorenflo, R.; Vivoli, A.; Mainardi, F. 4 2006 Mellin convolution for subordinated stable processes. Zbl 1411.60026Mainardi, F.; Pagnini, G.; Gorenflo, R. 3 2006 Fractional diffusion in inhomogeneous media. Zbl 1082.76097Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M. 99 2005 Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations. I. Zbl 1100.35132Umarov, Sabir; Gorenflo, Rudolf 36 2005 Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 21 2005 Discrete models of time-fractional diffusion in a potential well. Zbl 1129.26002Gorenflo, R.; Abdel-Rehim, E. A. 8 2005 On multi-dimensional random walk models approximating symmetric space-fractional diffusion processes. Zbl 1131.60038Umarov, Sabir; Gorenflo, Rudolf 8 2005 A fractional generalization of the Poisson processes. Zbl 1087.60064Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 72 2004 Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco 19 2004 From power laws to fractional diffusion: the direct way. Zbl 1086.60049Gorenflo, R.; Abdel-Rehim, Entsar A. 10 2004 Anomalous waiting times in high-frequency financial data. Zbl 1409.62216Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco 8 2004 A renewal process of Mittag-Leffler type. Zbl 1191.60101Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 4 2004 Distributed order time fractional diffusion equation. Zbl 1089.60046Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu. 87 2003 Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 27 2003 Fully discrete random walks for space-time fractional diffusion equations. Zbl 1145.60312Gorenflo, Rudolf; Vivoli, Alessandro 16 2003 Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco 12 2003 Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo 153 2002 Computation of the Mittag-Leffler function \(E_{\alpha,\beta}(z)\) and its derivative. Zbl 1027.33016Gorenflo, Rudolf; Loutchko, Joulia; Luchko, Yuri 113 2002 Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo 88 2002 Moment theory and some inverse problems in potential theory and heat conduction. Zbl 1005.30025Ang, Dang Dinh; Gorenflo, Rudolf; Le, Vy Khoi; Trong, Dang Duc 14 2002 The tomato salad problem in spherical stereology. Zbl 1049.45003Gorenflo, R. 1 2002 Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco 150 2001 Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082Gorenflo, Rudolf; Mainardi, Francesco 17 2001 On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005Mainardi, Francesco; Gorenflo, Rudolf 172 2000 Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 126 2000 Fractional calculus: Special functions and applications. Zbl 1030.26004Mainardi, F.; Gorenflo, R. 72 2000 Mapping between solutions of fractional diffusion-wave equations. Zbl 1033.35161Gorenflo, Rudolf; Iskenderov, Asaf; Luchko, Yuri 51 2000 On the Cauchy and multi-point problems for partial pseudo-differential equations of fractional order. Zbl 1033.35160Gorenflo, 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 1033.35162Gorenflo, Rudolf; Luchko, Yurii F.; Umarov, Sabir R. 3 2000 An operational method for solving fractional differential equations with the Caputo derivatives. Zbl 0931.44003Luchko, Yurii; Gorenflo, Rudolf 172 1999 Analytical properties and applications of the Wright function. Zbl 1027.33006Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 116 1999 Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006Gorenflo, R.; Mainardi, F. 38 1999 Operator theoretic treatment of linear Abel integral equations of first kind. Zbl 1306.47057Gorenflo, Rudolf; Yamamoto, Masahiro 25 1999 A multi-dimensional Hausdorff moment problems regularization by finite moments. Zbl 0921.65089Ang, D. D.; Gorenflo, R.; Trong, D. D. 10 1999 On solvability of linear fractional differential equations in Banach spaces. Zbl 1041.34045Gorenflo, R.; Luchko, Yu. F.; Zabrejko, P. P. 8 1999 On optimal regularization methods for fractional differentiation. Zbl 0941.65140Tautenhahn, U.; Gorenflo, R. 7 1999 On the autoconvolution equation and total variation constraints. Zbl 0923.65098Fleischer, G.; Gorenflo, R.; Hofmann, B. 2 1999 Random walk models for space-fractional diffusion processes. Zbl 0946.60039Gorenflo, R.; Mainardi, F. 133 1998 Scale-invariant solutions of a partial differential equation of fractional order. Zbl 0940.45001Luchko, Yu.; Gorenflo, R. 51 1998 Fractional calculus and stable probability distributions. Zbl 0934.35008Gorenflo, R.; Mainardi, F. 44 1998 On the generalized Mittag-Leffler type functions. Zbl 0935.33012Gorenflo, R.; Kilbas, A. A.; Rogosin, S. V. 42 1998 Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M. 34 1998 Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021Gorenflo, R.; Mainardi, F. 8 1998 On the properties of a generalized function of Mittag-Leffler type. Zbl 1039.33503Gorenflo, R.; Kilbas, A. A.; Rogozin, S. V. 1 1998 Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010Gorenflo, R.; Mainardi, F. 118 1997 Operational method for solving generalized Abel integral equation of second kind. Zbl 0887.44003Gorenflo, Rudolf; Luchko, Yuri 18 1997 Operational method for solving integral equations with Gauss’ hypergeometric function as a kernel. Zbl 0889.45005Gorenflo, R.; Luchko, Yu. F.; Srivastava, H. M. 5 1997 Locally controllable regularization of Abel integral equations via operator complementation. Zbl 0898.65096Gorenflo, Rudolf; Medvedeva, T.; Rubin, Boris 4 1997 On the dependence of asymptotics of \(S\)-numbers of fractional integration operators on weight functions. Zbl 0912.47011Gorenflo, R.; Samko, S. 2 1997 Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011Gorenflo, R.; Mainardi, F. 43 1996 Asymptotics of singular values of Volterra integral operators. Zbl 0858.47021Yu Kim Tuan; Gorenflo, Rudolf 5 1996 Extrapolation to the limit for numerical fractional differentiation. Zbl 0860.65011Vu Kim Tuan; Gorenflo, R. 21 1995 On ultraslow and intermediate processes. Zbl 0923.34005Gorenflo, R.; Rutman, R. 21 1995 Singular value decomposition of fractional integration operators in \(L_ 2\)-spaces with weights. Zbl 0824.45002Gorenflo, R.; Vu Kim Tuan 5 1995 Singular values of fractional and Volterra integral operators. Zbl 0829.45001Vu Kim Tuan; Gorenflo, Rudolf 3 1995 On asymptotic solutions of nonlinear Abel-Volterra integral equations with quasipolynomial free term. Zbl 0858.45007Kilbas, Anatoly A.; Saigo, Megumi; Gorenflo, Rudolf 3 1995 Regularization of a two-dimensional inverse Stefan problem. Zbl 0837.35148Gorenflo, R.; Ang, D. D.; Thanh, D. N. 2 1995 Asymptotic solution of a nonlinear Abel-Volterra integral equation of second kind. Zbl 0838.45004Gorenflo, Rudolf; Kilbas, Anatoly A. 2 1995 On regularized inversion of Abel integral operators. Zbl 0852.65132Gorenflo, Rudolf; Yamamoto, Masahiro 2 1995 Existence of global quasiclassical solutions to the Cauchy problem for Hamilton-Jacobi equations. Zbl 0856.35021Tran 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 0804.45003Gorenflo, Rudolf; Hofmann, Bernd 30 1994 Asymptotics of singular values of fractional integral operators. Zbl 0808.45001Vu Kim Tuan; Gorenflo, Rudolf 9 1994 On the regularization of fractional differentiation of arbitrary positive order. Zbl 0810.65137Vu Kim Tuan; Gorenflo, Rudolf 2 1994 The Grünwald-Letnikov difference operator and regularization of the Weyl fractional differentiation. Zbl 0804.65140Vu Kim Tuan; Gorenflo, R. 2 1994 Locally controllable regularization of fractional derivatives. Zbl 0815.65142Gorenflo, Rudolf; Rubin, Boris 2 1994 On nondegenerate and degenerate nonlinear Abel integral equations of the first kind. Zbl 0796.45008Dang Dinh Ang; Gorenflo, Rudolf 1 1994 On Abel type integral equations of first kind. Zbl 0807.45003Gorenflo, Rudolf; Kilbas, Anatoly A.; Yakubovich, Semen B. 1 1994 On the integral convolution for inverse \(G\)-transforms. Zbl 0885.44005Gorenflo, 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 2 1993 A regularization method for the moment problem. Zbl 0789.65095Ang, D. D.; Le, Vy Khoi; Gorenflo, R. 1 1993 Towards the Cauchy problem for the Laplace equation. Zbl 0820.35032Dinh Nho Hào; Tran Duc Van; Gorenflo, Rudolf 3 1992 Regularization of a generalized Abel integral equation. Zbl 0726.65154Dang 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 0717.45002Gorenflo, Rudolf; Vessella, Sergio 151 1991 On analysis and discretization of nonlinear Abel integral equations of first kind. Zbl 0883.65114Gorenflo, Rudolf; Pfeiffer, Andreas 3 1991 A noncharacteristic Cauchy problem for the heat equation. Zbl 0741.35090Dinh Nho Hào; Gorenflo, Rudolf 2 1991 On Sobolev-Orlicz spaces of infinite order for a full Euclidean space. Zbl 0727.46019Tran Duc Van; Ha Huy Bang; Gorenflo, R. 1 1991 ...and 21 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,998 Authors 55 Liu, Fawang 47 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. 22 Chen, Yangquan 22 Yamamoto, Masahiro 20 de Oliveira, Edmundo Capelas 20 Hofmann, Bernd 20 Luchko, Yuri 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 Lizama, Carlos 15 Luchko, Yurii F. 15 Machado, José António Tenreiro 15 Wang, Jinrong 15 Warma, Mahamadi 14 Kiryakova, Virginia S. 14 Sandev, Trifce 13 Abdeljawad, Thabet 13 Bulavatskyĭ, Volodymyr M. 13 Garra, Roberto 13 Jafari, Hossein 13 Odibat, Zaid M. 13 Saxena, Ram Kishore 13 Trujillo, Juan J. 13 Wang, Hong 12 Atanackovic, Teodor M. 12 Bhalekar, Sachin 12 Fernandez, Arran 12 Sun, Hongguang 12 Tatar, Nasser-eddine 11 Agarwal, Praveen 11 Atangana, Abdon 11 Chen, Wen 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 Xiong, Xiangtuan 11 Zheng, Xiangcheng 10 Ashurov, Ravshan Rajabovich 10 Budak, Hüseyin 10 Farid, Ghulam 10 Ge, Fudong 10 Giusti, Andrea 10 Kaltenbacher, Barbara 10 Li, Zhiyuan 10 Malik, Salman A. 10 Rogosin, Sergei V. 10 Sooppy Nisar, Kottakkaran 10 Sun, Haiwei 9 Deng, Weihua 9 Karniadakis, George Em 9 Mehrez, Khaled 9 Momani, Shaher M. 9 Roscani, Sabrina D. 9 Rundell, William 9 Ruzhansky, Michael V. 9 Trong, Dang Duc 9 Vanterler da Costa Sousa, José 9 Vellaisamy, Palaniappan 9 Wang, Yuanming 9 Xu, Chuanju 9 Zhou, Zhi 8 Bazhlekova, Emilia G. 8 Burrage, Kevin 8 Diethelm, Kai 8 Duan, Junsheng 8 Horzela, Andrzej 8 Janno, Jaan 8 Keyantuo, Valentin 8 Lazarov, Raytcho D. 8 Li, Changpin 8 Macci, Claudio 8 Mahmudov, Nazim Idrisoglu 8 Sarikaya, Mehmet Zeki 8 Stojanović, Mirjana N. 8 Tarasova, Valentina V. 8 Umarov, Sabir R. 8 Vieira, Nelson 8 Xu, Mingyu 8 Zaky, Mahmoud A. 8 Zayernouri, Mohsen ...and 2,898 more Authors all top 5 Cited in 420 Serials 188 Fractional Calculus & Applied Analysis 123 Applied Mathematics and Computation 97 Computers & Mathematics with Applications 89 Journal of Computational and Applied Mathematics 71 Advances in Difference Equations 63 Chaos, Solitons and Fractals 53 Journal of Computational Physics 51 Journal of Mathematical Analysis and Applications 48 Communications in Nonlinear Science and Numerical Simulation 38 Physica A 38 Nonlinear Dynamics 38 Abstract and Applied Analysis 36 Computational and Applied Mathematics 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 22 Applied Mathematical Modelling 20 Inverse Problems in Science and Engineering 19 Advances in Mathematical Physics 19 Mathematics 18 Mathematics and Computers in Simulation 18 International Journal of Applied and Computational Mathematics 17 Nonlinear Analysis. 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Theory and Methods 5 SIAM Journal on Applied Mathematics 5 Complexity 5 Methodology and Computing in Applied Probability 5 Communications on Pure and Applied Analysis 5 Journal of Physics A: Mathematical and Theoretical ...and 320 more Serials all top 5 Cited in 53 Fields 1,144 Partial differential equations (35-XX) 856 Real functions (26-XX) 856 Numerical analysis (65-XX) 564 Ordinary differential equations (34-XX) 362 Special functions (33-XX) 332 Probability theory and stochastic processes (60-XX) 301 Integral equations (45-XX) 182 Operator theory (47-XX) 121 Integral transforms, operational calculus (44-XX) 116 Statistical mechanics, structure of matter (82-XX) 101 Fluid mechanics (76-XX) 95 Mechanics of deformable solids (74-XX) 87 Systems theory; control (93-XX) 77 Biology and other natural sciences (92-XX) 60 Classical thermodynamics, heat transfer (80-XX) 55 Functions of a complex variable (30-XX) 47 Dynamical systems and ergodic theory (37-XX) 45 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 43 Calculus of variations and optimal control; optimization (49-XX) 42 Statistics (62-XX) 39 Harmonic analysis on Euclidean spaces (42-XX) 34 Approximations and expansions (41-XX) 34 Quantum theory (81-XX) 31 Functional analysis (46-XX) 21 Mechanics of particles and systems (70-XX) 21 Optics, electromagnetic theory (78-XX) 21 Operations research, mathematical programming (90-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 18 Information and communication theory, circuits (94-XX) 14 Difference and functional equations (39-XX) 14 Computer science (68-XX) 13 Measure and integration (28-XX) 13 Geophysics (86-XX) 11 Combinatorics (05-XX) 10 Potential theory (31-XX) 9 Sequences, series, summability (40-XX) 6 History and biography (01-XX) 6 Number theory (11-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Abstract harmonic analysis (43-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Differential geometry (53-XX) 3 General and overarching topics; collections (00-XX) 3 Convex and discrete geometry (52-XX) 2 Group theory and generalizations (20-XX) 2 Relativity and gravitational theory (83-XX) 2 Mathematics education (97-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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