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Mainardi, Francesco

Author ID: mainardi.francesco Recent zbMATH articles by "Mainardi, Francesco"
Published as: Mainardi, Francesco; Mainardi, F.
Homepage: http://www.fracalmo.org/mainardi/
External Links: ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef
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)

Publications by Year

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
2010
Fractals and fractional calculus in continuum mechanics. Zbl 0917.73004
Carpinteri, A.; Mainardi, F.
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
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.
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 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
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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. Series B
19 International Journal of Theoretical Physics
19 Statistics & Probability Letters
19 Cybernetics and Systems Analysis
19 Inverse Problems in Science and Engineering
18 Applicable Analysis
18 Computer Methods in Applied Mechanics and Engineering
18 Filomat
18 Journal of Physics A: Mathematical and Theoretical
17 Physics Letters. A
17 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
17 Nonlinear Analysis. Real World Applications
16 Turkish Journal of Mathematics
16 Journal of Applied Mathematics
16 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. 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
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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)
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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)
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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)
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