Edit Profile (opens in new tab) Mainardi, Francesco Compute Distance To: Compute Author ID: mainardi.francesco Published as: Mainardi, Francesco; Mainardi, F. External Links: Wikidata · IdRef Documents Indexed: 122 Publications since 1973, including 6 Books 5 Contributions as Editor Biographic References: 2 Publications Co-Authors: 55 Co-Authors with 105 Joint Publications 1,717 Co-Co-Authors all top 5 Co-Authors 17 single-authored 40 Gorenflo, Rudolf 19 Pagnini, Gianni 9 Giusti, Andrea 8 Mura, Antonio 7 Garrappa, Roberto 7 Rogosin, Sergei V. 6 Kiryakova, Virginia S. 6 Scalas, Enrico 6 Vivoli, Alessandro 5 Colombaro, Ivano 5 Machado, José António Tenreiro 5 Turchetti, Giorgio 4 Garra, Roberto 4 Luchko, Yuri 4 Paradisi, Paolo 4 Raberto, Marco 3 Consiglio, Armando 2 de Hoop, Adrianus T. 2 Guicking, Dieter 2 Guran, Ardéshir 2 Kilbas, Anatoliĭ Aleksandrovich 2 Masina, Enrico 2 Moretti, Daniele 2 Servizi, Graziano 2 Tampieri, Francesco 2 Van Groesen, Embrecht W. C. 1 Angelucci, M. G. 1 Apelblat, Alexander 1 Atanackovic, Teodor M. 1 Beghin, Luisa 1 Brilla, Jozef 1 Buchen, Peter W. 1 Buggisch, Hans Walter 1 Carcione, José M. 1 Castellani, Gastone C. 1 Cesari, Riccardo 1 de Oliveira, Edmundo Capelas 1 Dragonette, Louis R. 1 Engelbrecht, Jüri 1 Gaunaurd, Guillermo C. 1 Gebauer, K. 1 Graffi, Dario 1 Guido, Maione 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 Paris, Richard Bruce 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 Tocci, Donatella 1 Tomirotti, M. 1 Trautenberg, E. A. 1 Uberall, Herbert 1 Vaz, Jayme jun. 1 Vitali, Giorgio 1 Vitali, Giuliano 1 Vitali, Silvia 1 Zahorski, Stefan all top 5 Serials 22 Fractional Calculus & Applied Analysis 8 Journal of Computational and Applied Mathematics 4 Wave Motion 3 Physica A 3 Chaos, Solitons and Fractals 3 Meccanica 2 Computers & Mathematics with Applications 2 The Geophysical Journal of the Royal Astronomical Society 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 Journal of Mathematical 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 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 all top 5 Fields 63 Real functions (26-XX) 44 Special functions (33-XX) 38 Partial differential equations (35-XX) 38 Probability theory and stochastic processes (60-XX) 30 Mechanics of deformable solids (74-XX) 22 Integral equations (45-XX) 20 Integral transforms, operational calculus (44-XX) 18 Fluid mechanics (76-XX) 17 Ordinary differential equations (34-XX) 10 History and biography (01-XX) 6 General and overarching topics; collections (00-XX) 6 Numerical analysis (65-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Optics, electromagnetic theory (78-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Functions of a complex variable (30-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of particles and systems (70-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 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 108 Publications have been cited 6,600 times in 3,622 Documents Cited by ▼ Year ▼ Fractals and fractional calculus in continuum mechanics. Zbl 0917.73004Carpinteri, A.; Mainardi, F. 844 1997 Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004Mainardi, Francesco 825 2010 Mittag-Leffler functions, related topics and applications. Zbl 1309.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 462 2014 Recent history of fractional calculus. Zbl 1221.26002Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco 407 2011 The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni 344 2001 Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 1080.26505Mainardi, Francesco 296 1996 The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036Mainardi, F. 224 1996 Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033Raberto, Marco; Scalas, Enrico; Mainardi, Francesco 192 2002 On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005Mainardi, Francesco; Gorenflo, Rudolf 173 2000 Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo 157 2002 Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco 153 2001 Random walk models for space-fractional diffusion processes. Zbl 0946.60039Gorenflo, R.; Mainardi, F. 134 1998 Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010Gorenflo, R.; Mainardi, F. 132 1997 Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 128 2000 Analytical properties and applications of the Wright function. Zbl 1027.33006Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 119 1999 A new dissipation model based on memory mechanism. Zbl 1213.74005Caputo, M.; Mainardi, F. 106 2007 Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo 90 2002 Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 78 2007 Time-fractional diffusion of distributed order. Zbl 1229.35118Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 76 2008 Fractional calculus: Special functions and applications. Zbl 1030.26004Mainardi, F.; Gorenflo, R. 73 2000 A fractional generalization of the Poisson processes. Zbl 1087.60064Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico 72 2004 The Wright functions as solutions of the time-fractional diffusion equation. Zbl 1053.35008Mainardi, Francesco; Pagnini, Gianni 67 2003 Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004Gorenflo, Rudolf; Mainardi, Francesco 64 2009 The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 61 2010 Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro 51 2007 Fox \(H\) functions in fractional diffusion. Zbl 1061.33012Mainardi, Francesco; Pagnini, Gianni; Saxena, R. K. 48 2005 Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304Mainardi, Francesco; Gorenflo, Rudolf 47 2007 The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002Mainardi, Francesco; Pagnini, Gianni 47 2007 On some properties of the Mittag-Leffler function \(E_\alpha(-t^\alpha)\), completely monotone for \(t>0\) with \(0<\alpha<1\). Zbl 1303.26007Mainardi, Francesco 46 2014 Fractional calculus and stable probability distributions. Zbl 0934.35008Gorenflo, R.; Mainardi, F. 45 1998 Fractional diffusive waves. Zbl 1360.76272Mainardi, Francesco; Paradisi, Paolo 45 2001 Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011Gorenflo, R.; Mainardi, F. 44 1996 The two forms of fractional relaxation of distributed order. Zbl 1165.26302Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana 43 2007 An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005Mainardi, Francesco 42 2012 Models of dielectric relaxation based on completely monotone functions. Zbl 06663380Garrappa, Roberto; Mainardi, Francesco; Guido, Maione 40 2016 Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006Gorenflo, R.; Mainardi, F. 39 1999 A poster about the recent history of fractional calculus. Zbl 1221.26013Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 35 2010 Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M. 35 1998 Mittag-Leffler functions, related topics and applications. 2nd extended and updated edition. Zbl 1451.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 33 2020 A poster about the old history of fractional calculus. Zbl 1222.26015Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 32 2010 The fractional Fick’s law for non-local transport processes. Zbl 0978.82080Paradisi, P.; Cesari, R.; Mainardi, F.; Tampieri, F. 30 2001 On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085Mainardi, Francesco; Garrappa, Roberto 29 2015 A practical guide to Prabhakar fractional calculus. Zbl 1437.33019Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco 29 2020 Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy 28 2013 Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 27 2003 On a special function arising in the time fractional diffusion-wave equation. Zbl 0921.33010Mainardi, F.; Tomirotti, M. 27 1995 Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia 25 2015 Fractional relaxation with time-varying coefficient. Zbl 1305.26018Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni 25 2014 Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 21 2005 Fractional models of anomalous relaxation based on the Kilbas and Saigo function. Zbl 1307.34007de Oliveira, Edmundo Capelas; Mainardi, Francesco; Vaz, Jayme jun. 20 2014 A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 19 2017 Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco 19 2004 A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005Mura, Antonio; Mainardi, Francesco 18 2009 Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082Gorenflo, Rudolf; Mainardi, Francesco 18 2001 Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. Zbl 1050.33018Mainardi, Francesco; Pagnini, Gianni 15 2003 Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf 14 2007 On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 14 2017 A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023Giusti, Andrea; Mainardi, Francesco 13 2016 Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 13 2007 Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco 12 2003 Asymptotic expansion for transient viscoelastic waves. Zbl 0351.73033Buchen, Peter W.; Mainardi, Francesco 12 1975 Time fractional cable equation and applications in neurophysiology. Zbl 1374.92025Vitali, Silvia; Castellani, Gastone; Mainardi, Francesco 12 2017 Fractional calculus: D’où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016). Zbl 1351.26017Tenreiro Machado, José António; Mainardi, Francesco; Kiryakova, Virginia; Atanacković, Teodor 11 2016 Fractional relaxation of distributed order. Zbl 1167.26303Gorenflo, Rudolf; Mainardi, Francesco 10 2006 Applications of fractional calculus in mechanics. Zbl 1113.26303Mainardi, Francesco 10 1998 The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 10 2018 Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003Mainardi, Francesco 8 2004 Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021Gorenflo, R.; Mainardi, F. 8 1998 Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017Mainardi, Francesco; Pagnini, Gianni 8 2008 Energy propagation in dissipative systems. I: Centrovelocity for linear systems. Zbl 0687.73036Van Groesen, Embrecht; Mainardi, Francesco 8 1989 Anomalous waiting times in high-frequency financial data. Zbl 1409.62216Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco 8 2004 On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051Gorenflo, Rudolf; Mainardi, Francesco 7 2015 Evolution equations for the probabilistic generalization of the Voigt profile function. Zbl 1179.82008Pagnini, Gianni; Mainardi, Francesco 7 2010 On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco 7 2017 Parametric subordination in fractional diffusion processes. Zbl 1371.60135Gorenflo, Rudolf; Mainardi, Francesco 7 2012 Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 6 2013 George William Scott Blair – the pioneer of fractional calculus in rheology. Zbl 1329.01079Rogosin, Sergei; Mainardi, Francesco 6 2014 Scott-Blair models with time-varying viscosity. Zbl 1407.76007Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 6 2018 Variable-order fractional calculus: a change of perspective. Zbl 1471.26002Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco 5 2021 Energy velocity for hyperbolic dispersive waves. Zbl 0605.73020Mainardi, Francesco 5 1987 On Volterra functions and Ramanujan integrals. Zbl 1342.45001Garrappa, Roberto; Mainardi, Francesco 5 2016 Balance laws and centro velocity in dissipative systems. Zbl 0728.73001van Groesen, E.; Mainardi, F. 5 1990 The functions of the Wright type in fractional calculus. Zbl 1216.26004Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 5 2010 A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients. Zbl 06916883Mainardi, Francesco 4 2018 Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Zbl 1260.60163Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 4 2012 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 Wave propagation in viscoelastic media. Euromech Colloquium 127 ”Wave propagation in viscoelastic media”, held at Taormina, Sicily, Italy, in April 1980. Zbl 0493.73028 4 1982 Professor Rudolf Gorenflo and his contribution to fractional calculus. Zbl 1273.01048Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei 4 2011 Linear viscoelasticity. Zbl 1213.74076Mainardi, Francesco 3 2002 Mellin convolution for subordinated stable processes. Zbl 1411.60026Mainardi, F.; Pagnini, G.; Gorenflo, R. 3 2006 Signal velocity for transient waves in linear dissipative media. Zbl 0529.73027Mainardi, Francesco 3 1983 Editorial. Fractional calculus: theory and applications. Zbl 1427.00050 3 2018 On transient waves in linear viscoelasticity. Zbl 07213199Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 3 2017 On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053Mainardi, Francesco; Masina, Enrico 3 2018 On the evolution of fractional diffusive waves. Zbl 1469.35219Consiglio, Armando; Mainardi, Francesco 2 2021 A representation theorem in the dynamic theory of porous media. Zbl 0288.73083Boschi, E.; Mainardi, F. 2 1973 On shock-wave formation for blood flow in arteries. Zbl 0505.76140Mainardi, F.; Buggisch, H. 2 1982 On the relation between sources and initial conditions for the wave and diffusion equations. Zbl 1409.35130Carcione, José M.; Mainardi, Francesco 2 2017 On the asymptotics of Wright functions of the second kind. Zbl 1474.30015Paris, Richard B.; Consiglio, Armando; Mainardi, Francesco 1 2021 Variable-order fractional calculus: a change of perspective. Zbl 1471.26002Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco 5 2021 On the evolution of fractional diffusive waves. Zbl 1469.35219Consiglio, Armando; Mainardi, Francesco 2 2021 On the asymptotics of Wright functions of the second kind. Zbl 1474.30015Paris, Richard B.; Consiglio, Armando; Mainardi, Francesco 1 2021 Fractional diffusive waves in the Cauchy and signalling problems. Zbl 1472.35430Consiglio, Armando; Mainardi, Francesco 1 2021 Mittag-Leffler functions, related topics and applications. 2nd extended and updated edition. Zbl 1451.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 33 2020 A practical guide to Prabhakar fractional calculus. Zbl 1437.33019Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco 29 2020 The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 10 2018 Scott-Blair models with time-varying viscosity. Zbl 1407.76007Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco 6 2018 A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients. Zbl 06916883Mainardi, Francesco 4 2018 Editorial. Fractional calculus: theory and applications. Zbl 1427.00050 3 2018 On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053Mainardi, Francesco; Masina, Enrico 3 2018 A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 19 2017 On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 14 2017 Time fractional cable equation and applications in neurophysiology. Zbl 1374.92025Vitali, Silvia; Castellani, Gastone; Mainardi, Francesco 12 2017 On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco 7 2017 On transient waves in linear viscoelasticity. Zbl 07213199Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco 3 2017 On the relation between sources and initial conditions for the wave and diffusion equations. Zbl 1409.35130Carcione, José M.; Mainardi, Francesco 2 2017 Models of dielectric relaxation based on completely monotone functions. Zbl 06663380Garrappa, Roberto; Mainardi, Francesco; Guido, Maione 40 2016 A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023Giusti, Andrea; Mainardi, Francesco 13 2016 Fractional calculus: D’où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016). Zbl 1351.26017Tenreiro Machado, José António; Mainardi, Francesco; Kiryakova, Virginia; Atanacković, Teodor 11 2016 On Volterra functions and Ramanujan integrals. Zbl 1342.45001Garrappa, Roberto; Mainardi, Francesco 5 2016 On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085Mainardi, Francesco; Garrappa, Roberto 29 2015 Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia 25 2015 On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051Gorenflo, Rudolf; Mainardi, Francesco 7 2015 Mittag-Leffler functions, related topics and applications. Zbl 1309.33001Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V. 462 2014 On some properties of the Mittag-Leffler function \(E_\alpha(-t^\alpha)\), completely monotone for \(t>0\) with \(0<\alpha<1\). Zbl 1303.26007Mainardi, Francesco 46 2014 Fractional relaxation with time-varying coefficient. Zbl 1305.26018Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni 25 2014 Fractional models of anomalous relaxation based on the Kilbas and Saigo function. Zbl 1307.34007de Oliveira, Edmundo Capelas; Mainardi, Francesco; Vaz, Jayme jun. 20 2014 George William Scott Blair – the pioneer of fractional calculus in rheology. Zbl 1329.01079Rogosin, Sergei; Mainardi, Francesco 6 2014 Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Zbl 1381.35226Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy 28 2013 Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 6 2013 An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005Mainardi, Francesco 42 2012 Parametric subordination in fractional diffusion processes. Zbl 1371.60135Gorenflo, Rudolf; Mainardi, Francesco 7 2012 Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Zbl 1260.60163Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco 4 2012 Recent history of fractional calculus. Zbl 1221.26002Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco 407 2011 Professor Rudolf Gorenflo and his contribution to fractional calculus. Zbl 1273.01048Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei 4 2011 Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004Mainardi, Francesco 825 2010 The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 61 2010 A poster about the recent history of fractional calculus. Zbl 1221.26013Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 35 2010 A poster about the old history of fractional calculus. Zbl 1222.26015Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco 32 2010 Evolution equations for the probabilistic generalization of the Voigt profile function. Zbl 1179.82008Pagnini, Gianni; Mainardi, Francesco 7 2010 The functions of the Wright type in fractional calculus. Zbl 1216.26004Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni 5 2010 Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004Gorenflo, Rudolf; Mainardi, Francesco 64 2009 A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005Mura, Antonio; Mainardi, Francesco 18 2009 The legacy of A.Y. Khintchine’s work in probability theory. Zbl 1188.01027Rogosin, S.; Mainardi, F. 1 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 76 2008 Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017Mainardi, Francesco; Pagnini, Gianni 8 2008 A new dissipation model based on memory mechanism. Zbl 1213.74005Caputo, M.; Mainardi, F. 106 2007 Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 78 2007 Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro 51 2007 Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304Mainardi, Francesco; Gorenflo, Rudolf 47 2007 The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002Mainardi, Francesco; Pagnini, Gianni 47 2007 The two forms of fractional relaxation of distributed order. Zbl 1165.26302Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana 43 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 Foreword to the special “FCAA” issue dedicated to 40 years of Caputo derivative and to the 80th anniversary of Prof. Caputo. Zbl 1213.01087Mainardi, Francesco 1 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 Fox \(H\) functions in fractional diffusion. Zbl 1061.33012Mainardi, Francesco; Pagnini, Gianni; Saxena, R. K. 48 2005 Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro 21 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 Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003Mainardi, Francesco 8 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 The Wright functions as solutions of the time-fractional diffusion equation. Zbl 1053.35008Mainardi, Francesco; Pagnini, Gianni 67 2003 Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf 27 2003 Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. Zbl 1050.33018Mainardi, Francesco; Pagnini, Gianni 15 2003 Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco 12 2003 Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033Raberto, Marco; Scalas, Enrico; Mainardi, Francesco 192 2002 Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo 157 2002 Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo 90 2002 Linear viscoelasticity. Zbl 1213.74076Mainardi, Francesco 3 2002 The fundamental solutions of the time-fractional diffusion equation. Zbl 1068.35038Mainardi, Francesco; Pagnini, Gianni 1 2002 The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni 344 2001 Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco 153 2001 Fractional diffusive waves. Zbl 1360.76272Mainardi, Francesco; Paradisi, Paolo 45 2001 The fractional Fick’s law for non-local transport processes. Zbl 0978.82080Paradisi, P.; Cesari, R.; Mainardi, F.; Tampieri, F. 30 2001 Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082Gorenflo, Rudolf; Mainardi, Francesco 18 2001 Acoustic interactions with submerged elastic structures. In 3 parts. Part 3: Acoustic propagation and scattering, wavelets and time frequency analysis. With a foreword by Hans A. Bethe. A Herbert Überall Festschrift volume. Zbl 0971.00064 1 2001 On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005Mainardi, Francesco; Gorenflo, Rudolf 173 2000 Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 128 2000 Fractional calculus: Special functions and applications. Zbl 1030.26004Mainardi, F.; Gorenflo, R. 73 2000 Analytical properties and applications of the Wright function. Zbl 1027.33006Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco 119 1999 Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006Gorenflo, R.; Mainardi, F. 39 1999 Random walk models for space-fractional diffusion processes. Zbl 0946.60039Gorenflo, R.; Mainardi, F. 134 1998 Fractional calculus and stable probability distributions. Zbl 0934.35008Gorenflo, R.; Mainardi, F. 45 1998 Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M. 35 1998 Applications of fractional calculus in mechanics. Zbl 1113.26303Mainardi, Francesco 10 1998 Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021Gorenflo, R.; Mainardi, F. 8 1998 Fractals and fractional calculus in continuum mechanics. Zbl 0917.73004Carpinteri, A.; Mainardi, F. 844 1997 Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010Gorenflo, R.; Mainardi, F. 132 1997 On linear differential equations of fractional order. Zbl 0919.34010Mainardi, Francesco 1 1997 Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 1080.26505Mainardi, Francesco 296 1996 The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036Mainardi, F. 224 1996 Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011Gorenflo, R.; Mainardi, F. 44 1996 On a special function arising in the time fractional diffusion-wave equation. Zbl 0921.33010Mainardi, F.; Tomirotti, M. 27 1995 Dynamics of an impurity in a 1D periodic Burgers flow. Zbl 0841.76085Angelucci, M. G.; Tampieri, F.; Mainardi, F. 1 1994 ...and 8 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,230 Authors 105 Băleanu, Dumitru I. 66 Machado, José António Tenreiro 62 Mainardi, Francesco 59 Liu, Fawang 39 Tarasov, Vasily E. 37 Abdeljawad, Thabet 32 Chen, Yangquan 31 Povstenko, Yuriy Z. 30 Anh, Vo V. 30 de Oliveira, Edmundo Capelas 30 Turner, Ian William 29 Meerschaert, Mark Marvin 25 Leonenko, Nikolai N. 24 Gorenflo, Rudolf 24 Sun, Zhizhong 22 Atanackovic, Teodor M. 22 Pagnini, Gianni 22 Wang, Hong 21 Garrappa, Roberto 21 Jarad, Fahd 21 Momani, Shaher M. 21 Polito, Federico 20 Luchko, Yuri 20 Trujillo, Juan J. 19 Beghin, Luisa 19 Nguyen Huy Tuan 19 Zorica, Dusan 18 Deng, Weihua 18 Odibat, Zaid M. 18 Pilipović, Stevan 18 Sandev, Trifce 17 Garra, Roberto 17 Li, Changpin 17 Saxena, Ram Kishore 17 Sooppy Nisar, Kottakkaran 17 Srivastava, Hari Mohan 17 Sun, Haiwei 17 Tomovski, Živorad 16 Ansari, Alireza 16 Dehghan Takht Fooladi, Mehdi 16 Mathai, Arakaparampli Mathai 16 Wang, Jinrong 16 Warma, Mahamadi 16 Yang, Xiao-Jun 15 Agarwal, Ravi P. 15 Ahmad, Bashir 15 Giusti, Andrea 15 Kiryakova, Virginia S. 15 Lizama, Carlos 15 Nieto Roig, Juan Jose 15 Sun, Hongguang 15 Tang, Yifa 15 Zheng, Xiangcheng 14 Bhalekar, Sachin 14 Fernandez, Arran 14 Jafari, Hossein 14 Karniadakis, George Em 14 Lopes, António M. 14 Wei, Ting 14 Yamamoto, Masahiro 13 Agarwal, Praveen 13 Arqub, Omar Abu 13 Bulavatskyĭ, Volodymyr M. 13 Chen, Wen 13 Duan, Junsheng 13 Vanterler da Costa Sousa, José 12 Abbaszadeh, Mostafa 12 Al-saedi, Ahmed Eid Salem 12 Balachandran, Krishnan 12 Budak, Hüseyin 12 da Silva, José Luís 12 Daftardar-Gejji, Varsha 12 Jiang, Xiaoyun 12 Kaminski Lenzi, Ervin 12 Scalas, Enrico 12 Torres, Delfim Fernando Marado 12 Zaky, Mahmoud A. 11 Atangana, Abdon 11 Di Paola, Mario 11 Ge, Fudong 11 Luchko, Yurii F. 11 Mehrez, Khaled 11 Orsingher, Enzo 11 Ponce, Rodrigo F. 11 Sayevand, Khosro 11 Wu, Guocheng 11 Xu, Chuanju 10 Ashurov, Ravshan Rajabovich 10 Bazhlekova, Emilia G. 10 D’Ovidio, Mirko 10 Fečkan, Michal 10 Gómez-Aguilar, José Francisco 10 Górska, Katarzyna 10 Iyiola, Olaniyi Samuel 10 Konjik, Sanja 10 Liang, Yingjie 10 Macci, Claudio 10 Mahmudov, Nazim Idrisoglu 10 O’Regan, Donal 10 Rundell, William ...and 4,130 more Authors all top 5 Cited in 445 Serials 249 Fractional Calculus & Applied Analysis 146 Applied Mathematics and Computation 141 Advances in Difference Equations 136 Computers & Mathematics with Applications 123 Chaos, Solitons and Fractals 101 Communications in Nonlinear Science and Numerical Simulation 100 Journal of Computational and Applied Mathematics 82 Journal of Computational Physics 71 Nonlinear Dynamics 64 Physica A 60 Computational and Applied Mathematics 57 Abstract and Applied Analysis 56 Applied Numerical Mathematics 52 Journal of Mathematical Analysis and Applications 46 Journal of Mathematical Physics 41 Journal of Scientific Computing 40 Numerical Algorithms 38 Applied Mathematical Modelling 35 Mathematical Problems in Engineering 32 Integral Transforms and Special Functions 29 International Journal of Applied and Computational Mathematics 28 Mathematics and Computers in Simulation 28 Journal of Applied Mathematics and Computing 27 Applied Mathematics Letters 26 International Journal of Computer Mathematics 26 Advances in Mathematical Physics 26 Mathematics 25 Fractals 24 AIMS Mathematics 22 Chaos 21 Acta Mechanica 21 Meccanica 21 International Journal of Differential Equations 19 Journal of Statistical Physics 19 Journal of Function Spaces 18 Inverse Problems 18 Engineering Analysis with Boundary Elements 18 Boundary Value Problems 17 Statistics & Probability Letters 17 Stochastic Processes and their Applications 17 Journal of Inequalities and Applications 17 Discrete and Continuous Dynamical Systems. 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Second Series 7 Asian-European Journal of Mathematics 7 Advances in Applied Mathematics and Mechanics 7 Symmetry ...and 345 more Serials all top 5 Cited in 53 Fields 1,539 Partial differential equations (35-XX) 1,195 Real functions (26-XX) 1,031 Numerical analysis (65-XX) 911 Ordinary differential equations (34-XX) 420 Special functions (33-XX) 403 Probability theory and stochastic processes (60-XX) 303 Integral equations (45-XX) 257 Operator theory (47-XX) 219 Mechanics of deformable solids (74-XX) 194 Systems theory; control (93-XX) 163 Statistical mechanics, structure of matter (82-XX) 157 Fluid mechanics (76-XX) 146 Biology and other natural sciences (92-XX) 137 Integral transforms, operational calculus (44-XX) 90 Dynamical systems and ergodic theory (37-XX) 88 Calculus of variations and optimal control; optimization (49-XX) 72 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 71 Classical thermodynamics, heat transfer (80-XX) 59 Approximations and expansions (41-XX) 54 Functions of a complex variable (30-XX) 53 Quantum theory (81-XX) 52 Harmonic analysis on Euclidean spaces (42-XX) 45 Functional analysis (46-XX) 45 Statistics (62-XX) 41 Information and communication theory, circuits (94-XX) 39 Mechanics of particles and systems (70-XX) 36 Difference and functional equations (39-XX) 34 Optics, electromagnetic theory (78-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 23 Measure and integration (28-XX) 23 Operations research, mathematical programming (90-XX) 20 Computer science (68-XX) 17 Geophysics (86-XX) 15 Number theory (11-XX) 14 Combinatorics (05-XX) 12 Sequences, series, summability (40-XX) 12 Global analysis, analysis on manifolds (58-XX) 11 History and biography (01-XX) 9 Abstract harmonic analysis (43-XX) 7 General and overarching topics; collections (00-XX) 7 Potential theory (31-XX) 6 Several complex variables and analytic spaces (32-XX) 4 General topology (54-XX) 4 Mathematics education (97-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 2 Algebraic geometry (14-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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