Edit Profile (opens in new tab) Mainardi, Francesco Co-Author Distance Author ID: mainardi.francesco Published as: Mainardi, Francesco; Mainardi, F. Homepage: http://www.fracalmo.org/mainardi/ External Links: ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef Documents Indexed: 148 Publications since 1973, including 6 Books and 23 Additional arXiv Preprints 4 Contributions as Editor Biographic References: 2 Publications Co-Authors: 59 Co-Authors with 128 Joint Publications 1,987 Co-Co-Authors all top 5 Co-Authors 20 single-authored 44 Gorenflo, Rudolf 20 Pagnini, Gianni 12 Giusti, Andrea 10 Mura, Antonio 8 Rogosin, Sergei V. 7 Colombaro, Ivano 7 Garra, Roberto 7 Garrappa, Roberto 6 Kiryakova, Virginia S. 6 Scalas, Enrico 6 Vivoli, Alessandro 5 Consiglio, Armando 5 Luchko, Yuri 5 Machado, José António Tenreiro 5 Turchetti, Giorgio 4 Paradisi, Paolo 4 Raberto, Marco 4 Spada, Giorgio 3 Masina, Enrico 3 Tampieri, Francesco 2 Apelblat, Alexander 2 Beghin, Luisa 2 de Oliveira, Edmundo Capelas 2 Kilbas, Anatoliĭ Aleksandrovich 2 Moretti, Daniele 2 Paris, Richard Bruce 2 Servizi, Graziano 2 Tomirotti, Massimo 2 Van Groesen, Embrecht W. C. 2 Vaz, Jayme jun. 1 Angelucci, M. G. 1 Atanackovic, Teodor M. 1 Brilla, Jozef 1 Buchen, Peter W. 1 Buggisch, Hans Walter 1 Carcione, José M. 1 Castellani, Gastone C. 1 Cesari, Riccardo 1 de Hoop, Adrianus T. 1 Dragonette, Louis R. 1 Engelbrecht, Jüri 1 Gaunaurd, Guillermo C. 1 Gebauer, K. 1 Giraldi, Filippo 1 Graffi, Dario 1 Guicking, Dieter 1 Guido, Maione 1 Guran, Ardéshir 1 Haddow, J. B. 1 Jeffrey, Alan P. 1 LeBlond, Paul H. 1 Luchko, Yurii F. 1 Luckock, Hugh 1 Madigosky, Walter 1 Mantelli, Maurizio 1 Moodie, T. Bryant 1 Oldham, Keith B. 1 Pironi, Paolo 1 Polito, Federico 1 Popolizio, Marina 1 Povstenko, Yuriy Z. 1 Sackman, Jerome L. 1 Saxena, Ram Kishore 1 Srivastava, Hari Mohan 1 Stojanović, Mirjana N. 1 Strick, E. 1 Tait, Robert J. 1 Taqqu, Murad S. 1 Tocci, Donatella 1 Trautenberg, E. A. 1 Uberall, Herbert 1 Vitali, Giorgio 1 Vitali, Giuliano 1 Vitali, Silvia 1 Zahorski, Stefan all top 5 Serials 23 Fractional Calculus & Applied Analysis 8 Journal of Computational and Applied Mathematics 4 Wave Motion 4 Chaos, Solitons and Fractals 3 Physica A 3 Meccanica 2 Computers & Mathematics with Applications 2 The Geophysical Journal of the Royal Astronomical Society 2 Journal of Mathematical Physics 2 Applied Mathematics and Computation 2 Ricerche di Matematica 2 Applied Mathematics Letters 2 Journal of Mathematical Sciences (New York) 2 Integral Transforms and Special Functions 2 Journal of Vibration and Control 2 Nonlinear Dynamics 2 Communications in Nonlinear Science and Numerical Simulation 2 Mathematics 2 Springer Monographs in Mathematics 1 Archives of Mechanics 1 Journal of Computational Physics 1 Matimyás Matematika 1 Reports on Mathematical Physics 1 Rheologica Acta 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Analysis und ihre Anwendungen 1 Journal of Physics A: Mathematical and General 1 Theory of Probability and Mathematical Statistics 1 Fractals 1 Vietnam Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Analysis (München) 1 Quantitative Finance 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Computational Acoustics 1 Lecture Notes of TICMI 1 Journal de Mécanique 1 CISM International Centre for Mechanical Sciences. Courses and Lectures 1 Series on Stability, Vibration and Control Systems. Series B 1 International Journal of Differential Equations 1 International Journal of Stochastic Analysis 1 Communications in Applied and Industrial Mathematics 1 Axioms 1 ICCM Notices 1 SEMA SIMAI Springer Series 1 Research Notes in Mathematics (San Francisco) all top 5 Fields 77 Real functions (26-XX) 61 Special functions (33-XX) 48 Probability theory and stochastic processes (60-XX) 42 Partial differential equations (35-XX) 38 Mechanics of deformable solids (74-XX) 36 Integral transforms, operational calculus (44-XX) 31 Integral equations (45-XX) 28 Fluid mechanics (76-XX) 19 Ordinary differential equations (34-XX) 11 History and biography (01-XX) 6 Numerical analysis (65-XX) 5 General and overarching topics; collections (00-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Functions of a complex variable (30-XX) 4 Optics, electromagnetic theory (78-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of particles and systems (70-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geophysics (86-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Potential theory (31-XX) 1 Operator theory (47-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 112 Publications have been cited 8,279 times in 5,308 Documents Cited by ▼ Year ▼ Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004 Mainardi, Francesco 1,038 2010 Fractals and fractional calculus in continuum mechanics. Zbl 0917.73004 Carpinteri, A.; Mainardi, F. 1,003 1997 Mittag-Leffler functions, related topics and applications. Zbl 1309.33001 Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 603 2014 Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010 Gorenflo, R.; Mainardi, F. 494 1997 Recent history of fractional calculus. Zbl 1221.26002 Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco 473 2011 The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156 Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni 383 2001 Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 1080.26505 Mainardi, Francesco 351 1996 The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036 Mainardi, F. 267 1996 Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033 Raberto, Marco; Scalas, Enrico; Mainardi, Francesco 209 2002 Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444 Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco 192 2001 On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005 Mainardi, Francesco; Gorenflo, Rudolf 189 2000 Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016 Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo 182 2002 Random walk models for space-fractional diffusion processes. Zbl 0946.60039 Gorenflo, R.; Mainardi, F. 144 1998 A new dissipation model based on memory mechanism. Zbl 1213.74005 Caputo, M.; Mainardi, F. 144 2007 Analytical properties and applications of the Wright function. Zbl 1027.33006 Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 136 1999 Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012 Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 132 2000 Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037 Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo 102 2002 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. 99 2020 Time-fractional diffusion of distributed order. Zbl 1229.35118 Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 97 2008 A fractional generalization of the Poisson processes. Zbl 1087.60064 Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 88 2004 Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004 Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 86 2007 Fractional calculus: Special functions and applications. Zbl 1030.26004 Mainardi, F.; Gorenflo, R. 75 2000 The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060 Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 75 2010 The Wright functions as solutions of the time-fractional diffusion equation. Zbl 1053.35008 Mainardi, Francesco; Pagnini, Gianni 74 2003 Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004 Gorenflo, Rudolf; Mainardi, Francesco 67 2009 On some properties of the Mittag-Leffler function \(E_\alpha(-t^\alpha)\), completely monotone for \(t>0\) with \(0<\alpha<1\). Zbl 1303.26007 Mainardi, Francesco 63 2014 Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304 Mainardi, Francesco; Gorenflo, Rudolf 58 2007 Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363 Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro 58 2007 An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005 Mainardi, Francesco 58 2012 Fractional diffusive waves. Zbl 1360.76272 Mainardi, Francesco; Paradisi, Paolo 56 2001 The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002 Mainardi, Francesco; Pagnini, Gianni 53 2007 Fox \(H\) functions in fractional diffusion. Zbl 1061.33012 Mainardi, Francesco; Pagnini, Gianni; Saxena, R. K. 53 2005 Models of dielectric relaxation based on completely monotone functions. Zbl 1499.78010 Garrappa, Roberto; Mainardi, Francesco; Guido, Maione 51 2016 The two forms of fractional relaxation of distributed order. Zbl 1165.26302 Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana 50 2007 Fractional calculus and stable probability distributions. Zbl 0934.35008 Gorenflo, R.; Mainardi, F. 48 1998 Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011 Gorenflo, R.; Mainardi, F. 48 1996 A practical guide to Prabhakar fractional calculus. Zbl 1437.33019 Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco 46 2020 Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009 Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M. 40 1998 Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006 Gorenflo, R.; Mainardi, F. 40 1999 The fractional Fick’s law for non-local transport processes. Zbl 0978.82080 Paradisi, P.; Cesari, R.; Mainardi, F.; Tampieri, F. 38 2001 A poster about the recent history of fractional calculus. Zbl 1221.26013 Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 36 2010 On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085 Mainardi, Francesco; Garrappa, Roberto 35 2015 A poster about the old history of fractional calculus. Zbl 1222.26015 Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 34 2010 Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226 Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy 33 2013 Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032 Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 31 2003 Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011 Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia 30 2015 On a special function arising in the time fractional diffusion-wave equation. Zbl 0921.33010 Mainardi, F.; Tomirotti, M. 29 1995 Fractional relaxation with time-varying coefficient. Zbl 1305.26018 Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni 29 2014 A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005 Mura, Antonio; Mainardi, Francesco 25 2009 Fractional models of anomalous relaxation based on the Kilbas and Saigo function. Zbl 1307.34007 de Oliveira, Edmundo Capelas; Mainardi, Francesco; Vaz, Jayme jun. 25 2014 Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070 Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 23 2005 A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019 Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 23 2017 Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082 Gorenflo, Rudolf; Mainardi, Francesco 22 2001 Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067 Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco 21 2004 Variable-order fractional calculus: a change of perspective. Zbl 1471.26002 Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco 21 2021 A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023 Giusti, Andrea; Mainardi, Francesco 17 2016 On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028 Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 17 2017 Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082 Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 16 2007 Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004 Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 16 2007 Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. Zbl 1050.33018 Mainardi, Francesco; Pagnini, Gianni 16 2003 Asymptotic expansion for transient viscoelastic waves. Zbl 0351.73033 Buchen, Peter W.; Mainardi, Francesco 15 1975 The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314 Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 15 2018 Applications of fractional calculus in mechanics. Zbl 1113.26303 Mainardi, Francesco 13 1998 Fractional calculus: D’où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016). Zbl 1351.26017 Tenreiro Machado, José António; Mainardi, Francesco; Kiryakova, Virginia; Atanacković, Teodor 13 2016 On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051 Gorenflo, Rudolf; Mainardi, Francesco 13 2015 Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163 Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco 12 2003 Time fractional cable equation and applications in neurophysiology. Zbl 1374.92025 Vitali, Silvia; Castellani, Gastone; Mainardi, Francesco 12 2017 On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019 Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco 11 2017 Fractional relaxation of distributed order. Zbl 1167.26303 Gorenflo, Rudolf; Mainardi, Francesco 10 2006 Parametric subordination in fractional diffusion processes. Zbl 1371.60135 Gorenflo, Rudolf; Mainardi, Francesco 10 2012 On transient waves in linear viscoelasticity. Zbl 1524.74079 Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 10 2017 Anomalous waiting times in high-frequency financial data. Zbl 1409.62216 Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco 10 2004 Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017 Mainardi, Francesco; Pagnini, Gianni 9 2008 Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. 2nd edition. Zbl 1495.26006 Mainardi, Francesco 9 2022 Energy propagation in dissipative systems. I: Centrovelocity for linear systems. Zbl 0687.73036 Van Groesen, Embrecht; Mainardi, Francesco 8 1989 Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021 Gorenflo, R.; Mainardi, F. 8 1998 Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003 Mainardi, Francesco 8 2004 On Volterra functions and Ramanujan integrals. Zbl 1342.45001 Garrappa, Roberto; Mainardi, Francesco 8 2016 Scott-Blair models with time-varying viscosity. Zbl 1407.76007 Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 8 2018 Evolution equations for the probabilistic generalization of the Voigt profile function. Zbl 1179.82008 Pagnini, Gianni; Mainardi, Francesco 7 2010 Balance laws and centro velocity in dissipative systems. Zbl 0728.73001 van Groesen, E.; Mainardi, F. 7 1990 George William Scott Blair – the pioneer of fractional calculus in rheology. Zbl 1329.01079 Rogosin, Sergei; Mainardi, Francesco 7 2014 Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116 Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 7 2013 The functions of the Wright type in fractional calculus. Zbl 1216.26004 Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 6 2010 Energy velocity for hyperbolic dispersive waves. Zbl 0605.73020 Mainardi, Francesco 6 1987 On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053 Mainardi, Francesco; Masina, Enrico 6 2018 Professor Rudolf Gorenflo and his contribution to fractional calculus. Zbl 1273.01048 Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei 6 2011 Wave propagation in viscoelastic media. Euromech Colloquium 127 ”Wave propagation in viscoelastic media”, held at Taormina, Sicily, Italy, in April 1980. Zbl 0493.73028 5 1982 A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients. Zbl 1499.34071 Mainardi, Francesco 5 2018 Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Zbl 1260.60163 Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 5 2012 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 On the evolution of fractional diffusive waves. Zbl 1469.35219 Consiglio, Armando; Mainardi, Francesco 4 2021 Signal velocity for transient waves in linear dissipative media. Zbl 0529.73027 Mainardi, Francesco 3 1983 The fundamental solutions of the time-fractional diffusion equation. Zbl 1068.35038 Mainardi, Francesco; Pagnini, Gianni 3 2002 Linear viscoelasticity. Zbl 1213.74076 Mainardi, Francesco 3 2002 Mellin convolution for subordinated stable processes. Zbl 1411.60026 Mainardi, F.; Pagnini, G.; Gorenflo, R. 3 2006 On the relation between sources and initial conditions for the wave and diffusion equations. Zbl 1409.35130 Carcione, José M.; Mainardi, Francesco 3 2017 Fractional diffusive waves in the Cauchy and signalling problems. Zbl 1472.35430 Consiglio, Armando; Mainardi, Francesco 3 2021 Editorial. Fractional calculus: theory and applications. Zbl 1427.00050 3 2018 Truncated generalized coherent states. Zbl 1511.81076 Giraldi, Filippo; Mainardi, Francesco 1 2023 Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. 2nd edition. Zbl 1495.26006 Mainardi, Francesco 9 2022 Wright functions of the second kind and Whittaker functions. Zbl 1503.33006 Mainardi, Francesco; Paris, Richard B.; Consiglio, Armando 1 2022 Variable-order fractional calculus: a change of perspective. Zbl 1471.26002 Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco 21 2021 On the evolution of fractional diffusive waves. Zbl 1469.35219 Consiglio, Armando; Mainardi, Francesco 4 2021 Fractional diffusive waves in the Cauchy and signalling problems. Zbl 1472.35430 Consiglio, Armando; Mainardi, Francesco 3 2021 On the asymptotics of Wright functions of the second kind. Zbl 1474.30015 Paris, Richard B.; Consiglio, Armando; Mainardi, Francesco 2 2021 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. 99 2020 A practical guide to Prabhakar fractional calculus. Zbl 1437.33019 Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco 46 2020 Applications of the Efros theorem to the Wright functions of the second kind and other results. Zbl 1513.33013 Apelblat, Alexander; Mainardi, Francesco 1 2020 The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314 Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 15 2018 Scott-Blair models with time-varying viscosity. Zbl 1407.76007 Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 8 2018 On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053 Mainardi, Francesco; Masina, Enrico 6 2018 A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients. Zbl 1499.34071 Mainardi, Francesco 5 2018 Editorial. Fractional calculus: theory and applications. Zbl 1427.00050 3 2018 A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019 Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 23 2017 On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028 Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 17 2017 Time fractional cable equation and applications in neurophysiology. Zbl 1374.92025 Vitali, Silvia; Castellani, Gastone; Mainardi, Francesco 12 2017 On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019 Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco 11 2017 On transient waves in linear viscoelasticity. Zbl 1524.74079 Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 10 2017 On the relation between sources and initial conditions for the wave and diffusion equations. Zbl 1409.35130 Carcione, José M.; Mainardi, Francesco 3 2017 Models of dielectric relaxation based on completely monotone functions. Zbl 1499.78010 Garrappa, Roberto; Mainardi, Francesco; Guido, Maione 51 2016 A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023 Giusti, Andrea; Mainardi, Francesco 17 2016 Fractional calculus: D’où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016). Zbl 1351.26017 Tenreiro Machado, José António; Mainardi, Francesco; Kiryakova, Virginia; Atanacković, Teodor 13 2016 On Volterra functions and Ramanujan integrals. Zbl 1342.45001 Garrappa, Roberto; Mainardi, Francesco 8 2016 On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085 Mainardi, Francesco; Garrappa, Roberto 35 2015 Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011 Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia 30 2015 On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051 Gorenflo, Rudolf; Mainardi, Francesco 13 2015 Mittag-Leffler functions, related topics and applications. Zbl 1309.33001 Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 603 2014 On some properties of the Mittag-Leffler function \(E_\alpha(-t^\alpha)\), completely monotone for \(t>0\) with \(0<\alpha<1\). Zbl 1303.26007 Mainardi, Francesco 63 2014 Fractional relaxation with time-varying coefficient. Zbl 1305.26018 Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni 29 2014 Fractional models of anomalous relaxation based on the Kilbas and Saigo function. Zbl 1307.34007 de Oliveira, Edmundo Capelas; Mainardi, Francesco; Vaz, Jayme jun. 25 2014 George William Scott Blair – the pioneer of fractional calculus in rheology. Zbl 1329.01079 Rogosin, Sergei; Mainardi, Francesco 7 2014 Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226 Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy 33 2013 Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116 Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 7 2013 An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005 Mainardi, Francesco 58 2012 Parametric subordination in fractional diffusion processes. Zbl 1371.60135 Gorenflo, Rudolf; Mainardi, Francesco 10 2012 Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Zbl 1260.60163 Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 5 2012 Recent history of fractional calculus. Zbl 1221.26002 Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco 473 2011 Professor Rudolf Gorenflo and his contribution to fractional calculus. Zbl 1273.01048 Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei 6 2011 Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004 Mainardi, Francesco 1,038 2010 The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060 Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 75 2010 A poster about the recent history of fractional calculus. Zbl 1221.26013 Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 36 2010 A poster about the old history of fractional calculus. Zbl 1222.26015 Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 34 2010 Evolution equations for the probabilistic generalization of the Voigt profile function. Zbl 1179.82008 Pagnini, Gianni; Mainardi, Francesco 7 2010 The functions of the Wright type in fractional calculus. Zbl 1216.26004 Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 6 2010 Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004 Gorenflo, Rudolf; Mainardi, Francesco 67 2009 A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005 Mura, Antonio; Mainardi, Francesco 25 2009 The legacy of A.Y. Khintchine’s work in probability theory. Zbl 1188.01027 Rogosin, S.; Mainardi, F. 1 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 97 2008 Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017 Mainardi, Francesco; Pagnini, Gianni 9 2008 A new dissipation model based on memory mechanism. Zbl 1213.74005 Caputo, M.; Mainardi, F. 144 2007 Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004 Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 86 2007 Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304 Mainardi, Francesco; Gorenflo, Rudolf 58 2007 Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363 Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro 58 2007 The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002 Mainardi, Francesco; Pagnini, Gianni 53 2007 The two forms of fractional relaxation of distributed order. Zbl 1165.26302 Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana 50 2007 Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082 Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 16 2007 Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004 Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 16 2007 Foreword to the special “FCAA” issue dedicated to 40 years of Caputo derivative and to the 80th anniversary of Prof. Caputo. Zbl 1213.01087 Mainardi, Francesco 1 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 Fox \(H\) functions in fractional diffusion. Zbl 1061.33012 Mainardi, Francesco; Pagnini, Gianni; Saxena, R. K. 53 2005 Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070 Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 23 2005 A fractional generalization of the Poisson processes. Zbl 1087.60064 Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 88 2004 Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067 Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco 21 2004 Anomalous waiting times in high-frequency financial data. Zbl 1409.62216 Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco 10 2004 Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003 Mainardi, Francesco 8 2004 A renewal process of Mittag-Leffler type. Zbl 1191.60101 Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 4 2004 The Wright functions as solutions of the time-fractional diffusion equation. Zbl 1053.35008 Mainardi, Francesco; Pagnini, Gianni 74 2003 Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032 Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 31 2003 Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. Zbl 1050.33018 Mainardi, Francesco; Pagnini, Gianni 16 2003 Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163 Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco 12 2003 Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033 Raberto, Marco; Scalas, Enrico; Mainardi, Francesco 209 2002 Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016 Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo 182 2002 Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037 Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo 102 2002 The fundamental solutions of the time-fractional diffusion equation. Zbl 1068.35038 Mainardi, Francesco; Pagnini, Gianni 3 2002 Linear viscoelasticity. Zbl 1213.74076 Mainardi, Francesco 3 2002 The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156 Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni 383 2001 Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444 Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco 192 2001 Fractional diffusive waves. Zbl 1360.76272 Mainardi, Francesco; Paradisi, Paolo 56 2001 The fractional Fick’s law for non-local transport processes. Zbl 0978.82080 Paradisi, P.; Cesari, R.; Mainardi, F.; Tampieri, F. 38 2001 Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082 Gorenflo, Rudolf; Mainardi, Francesco 22 2001 On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005 Mainardi, Francesco; Gorenflo, Rudolf 189 2000 Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012 Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 132 2000 Fractional calculus: Special functions and applications. Zbl 1030.26004 Mainardi, F.; Gorenflo, R. 75 2000 Analytical properties and applications of the Wright function. Zbl 1027.33006 Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 136 1999 Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006 Gorenflo, R.; Mainardi, F. 40 1999 Random walk models for space-fractional diffusion processes. Zbl 0946.60039 Gorenflo, R.; Mainardi, F. 144 1998 Fractional calculus and stable probability distributions. Zbl 0934.35008 Gorenflo, R.; Mainardi, F. 48 1998 Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009 Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M. 40 1998 Applications of fractional calculus in mechanics. Zbl 1113.26303 Mainardi, Francesco 13 1998 Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021 Gorenflo, R.; Mainardi, F. 8 1998 Fractals and fractional calculus in continuum mechanics. Zbl 0917.73004 Carpinteri, A.; Mainardi, F. 1,003 1997 Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010 Gorenflo, R.; Mainardi, F. 494 1997 On linear differential equations of fractional order. Zbl 0919.34010 Mainardi, Francesco 1 1997 Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 1080.26505 Mainardi, Francesco 351 1996 The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036 Mainardi, F. 267 1996 ...and 12 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,879 Authors 146 Băleanu, Dumitru I. 79 Machado, José António Tenreiro 68 Mainardi, Francesco 64 Liu, Fawang 56 Momani, Shaher M. 54 Tarasov, Vasily E. 52 Abdeljawad, Thabet 35 Ahmad, Bashir 35 Chen, Yangquan 34 Anh, Vo V. 33 Povstenko, Yuriy Z. 33 Turner, Ian William 32 Al-saedi, Ahmed Eid Salem 32 de Oliveira, Edmundo Capelas 32 Wang, Hong 30 Odibat, Zaid M. 29 Budak, Hüseyin 29 Meerschaert, Mark Marvin 29 Sun, Zhizhong 29 Zhou, Yong 28 Agarwal, Ravi P. 28 Garrappa, Roberto 28 Leonenko, Nikolai N. 28 Sooppy Nisar, Kottakkaran 28 Trujillo, Juan J. 27 Atanackovic, Teodor M. 27 Nguyen Huy Tuan 27 Nieto Roig, Juan Jose 25 Pagnini, Gianni 25 Zheng, Xiangcheng 24 Gorenflo, Rudolf 24 Jarad, Fahd 23 Fernandez, Arran 23 Polito, Federico 23 Wei, Ting 22 Garra, Roberto 22 Karniadakis, George Em 21 Deng, Weihua 21 Li, Changpin 21 Luchko, Yuri 21 Pilipović, Stevan 21 Sandev, Trifce 21 Sun, Haiwei 21 Wang, Jinrong 21 Zorica, Dusan 20 Beghin, Luisa 20 Tomovski, Živorad 19 Ansari, Alireza 19 Benchohra, Mouffak 19 Cuevas, Claudio 19 Giusti, Andrea 19 Lizama, Carlos 19 Shah, Kamal 19 Srivastava, Hari Mohan 19 Yamamoto, Masahiro 19 Zaky, Mahmoud A. 18 Bulavatskyĭ, Volodymyr M. 18 Chen, Wen 18 Dehghan Takht Fooladi, Mehdi 18 Gómez-Aguilar, José Francisco 18 Vanterler da Costa Sousa, José 17 Agarwal, Praveen 17 Ntouyas, Sotiris K. 17 Sarikaya, Mehmet Zeki 17 Saxena, Ram Kishore 17 Scalas, Enrico 17 Warma, Mahamadi 16 Jafari, Hossein 16 Lopes, António M. 16 Metzler, Ralf 16 Set, Erhan 16 Tang, Yifa 16 Torres, Delfim Fernando Marado 16 Yang, Xiao-Jun 15 Arqub, Omar Abu 15 Atangana, Abdon 15 Kirane, Mokhtar 15 Kumar, Devendra 15 Li, Zhiyuan 15 Mahmudov, Nazim Idrisoglu 15 Malik, Salman A. 15 Mathai, Arakaparampli Mathai 15 Ordokhani, Yadollah 15 Sun, Hongguang 14 Balachandran, Krishnan 14 Bhrawy, Ali Hassan 14 Chechkin, Aleksei V. 14 Di Paola, Mario 14 Duan, Junsheng 14 El-Sayed, Ahmed Mohamed Ahmed 14 Kiryakova, Virginia S. 14 Kumar, Sunil 14 Liu, Yuji 14 Mehrez, Khaled 14 Razzaghi, Mohsen 14 Salahshour, Soheil 14 Wu, Guocheng 14 Zayernouri, Mohsen 13 Abdel-Rehim, Entsar A. 13 da Silva, José Luís ...and 5,779 more Authors all top 5 Cited in 537 Serials 339 Fractional Calculus & Applied Analysis 194 Applied Mathematics and Computation 186 Computers & Mathematics with Applications 183 Advances in Difference Equations 157 Chaos, Solitons and Fractals 151 Communications in Nonlinear Science and Numerical Simulation 137 Journal of Computational and Applied Mathematics 95 Journal of Computational Physics 95 Nonlinear Dynamics 94 Mathematical Methods in the Applied Sciences 85 Physica A 85 Abstract and Applied Analysis 84 Computational and Applied Mathematics 70 Applied Numerical Mathematics 67 Journal of Mathematical Analysis and Applications 63 Applied Mathematical Modelling 61 Journal of Mathematical Physics 56 Numerical Algorithms 55 Journal of Scientific Computing 47 Fractals 44 Mathematical Problems in Engineering 41 Applied Mathematics Letters 41 Integral Transforms and Special Functions 41 International Journal of Applied and Computational Mathematics 40 Numerical Methods for Partial Differential Equations 40 Journal of Applied Mathematics and Computing 39 Mathematics and Computers in Simulation 39 International Journal of Computer Mathematics 37 Boundary Value Problems 37 Advances in Mathematical Physics 33 Meccanica 33 Journal of Function Spaces 31 Journal of Inequalities and Applications 31 Fractional Differential Calculus 30 AIMS Mathematics 29 Mathematics 28 Acta Mechanica 27 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 27 International Journal of Differential Equations 25 Inverse Problems 24 Chaos 24 International Journal of Nonlinear Sciences and Numerical Simulation 22 Journal of Statistical Physics 22 Engineering Analysis with Boundary Elements 22 Lobachevskii Journal of Mathematics 21 Journal of Differential Equations 21 Mediterranean Journal of Mathematics 21 Mathematical Modelling of Natural Phenomena 21 Discrete and Continuous Dynamical Systems. Series S 20 ZAMP. Zeitschrift für angewandte Mathematik und Physik 20 Stochastic Processes and their Applications 20 SIAM Journal on Scientific Computing 20 Discrete and Continuous Dynamical Systems. 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RACSAM 15 Journal of Mathematical Sciences (New York) 15 Journal of Vibration and Control 15 Differential Equations and Dynamical Systems 15 Journal of Nonlinear Science and Applications 15 Evolution Equations and Control Theory 14 SIAM Journal on Numerical Analysis 14 Stochastic Analysis and Applications 14 Journal of Evolution Equations 14 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 14 Mathematical Sciences 13 Journal of the Franklin Institute 13 Reports on Mathematical Physics 13 Discrete Dynamics in Nature and Society 13 Waves in Random and Complex Media 13 Journal of Mathematics 12 Journal of Integral Equations and Applications 12 Computational Methods for Differential Equations 11 Journal of Inverse and Ill-Posed Problems 11 Advances in Computational Mathematics 11 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 11 Differential Equations 11 Asian-European Journal of Mathematics 11 S\(\vec{\text{e}}\)MA Journal 11 Axioms 11 East Asian Journal on Applied Mathematics 10 Ukrainian Mathematical Journal 10 Mathematics and Mechanics of Solids 10 Qualitative Theory of Dynamical Systems 10 Computational Methods in Applied Mathematics 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Journal of Applied Nonlinear Dynamics 10 Journal of Mathematical Modeling 10 Vestnik KRAUNTS. Fiziko-Matematicheskie Nauki ...and 437 more Serials all top 5 Cited in 53 Fields 2,187 Partial differential equations (35-XX) 1,790 Real functions (26-XX) 1,514 Ordinary differential equations (34-XX) 1,512 Numerical analysis (65-XX) 563 Special functions (33-XX) 537 Probability theory and stochastic processes (60-XX) 458 Integral equations (45-XX) 438 Operator theory (47-XX) 319 Mechanics of deformable solids (74-XX) 287 Systems theory; control (93-XX) 218 Biology and other natural sciences (92-XX) 217 Fluid mechanics (76-XX) 203 Integral transforms, operational calculus (44-XX) 192 Statistical mechanics, structure of matter (82-XX) 150 Calculus of variations and optimal control; optimization (49-XX) 131 Dynamical systems and ergodic theory (37-XX) 92 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 87 Classical thermodynamics, heat transfer (80-XX) 83 Quantum theory (81-XX) 81 Approximations and expansions (41-XX) 76 Harmonic analysis on Euclidean spaces (42-XX) 74 Functions of a complex variable (30-XX) 62 Statistics (62-XX) 62 Mechanics of particles and systems (70-XX) 57 Functional analysis (46-XX) 55 Difference and functional equations (39-XX) 52 Information and communication theory, circuits (94-XX) 47 Optics, electromagnetic theory (78-XX) 44 Measure and integration (28-XX) 32 Linear and multilinear algebra; matrix theory (15-XX) 32 Operations research, mathematical programming (90-XX) 29 Global analysis, analysis on manifolds (58-XX) 27 Computer science (68-XX) 25 Geophysics (86-XX) 21 Number theory (11-XX) 15 Combinatorics (05-XX) 15 Relativity and gravitational theory (83-XX) 14 Abstract harmonic analysis (43-XX) 13 Sequences, series, summability (40-XX) 12 Several complex variables and analytic spaces (32-XX) 11 History and biography (01-XX) 10 Potential theory (31-XX) 9 Differential geometry (53-XX) 7 General and overarching topics; collections (00-XX) 6 General topology (54-XX) 3 Mathematics education (97-XX) 2 Algebraic geometry (14-XX) 2 Algebraic topology (55-XX) 2 Astronomy and astrophysics (85-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Topological groups, Lie groups (22-XX) 1 Convex and discrete geometry (52-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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