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Mainardi, Francesco

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Author ID: mainardi.francesco Recent zbMATH articles by "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
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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

Publications by Year

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 0917.73004
Carpinteri, A.; Mainardi, F.
844
1997
Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004
Mainardi, Francesco
825
2010
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
462
2014
Recent history of fractional calculus. Zbl 1221.26002
Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco
407
2011
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
344
2001
Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 1080.26505
Mainardi, Francesco
296
1996
The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036
Mainardi, F.
224
1996
Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033
Raberto, Marco; Scalas, Enrico; Mainardi, Francesco
192
2002
On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
173
2000
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
157
2002
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
153
2001
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
134
1998
Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010
Gorenflo, R.; Mainardi, F.
132
1997
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
128
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
119
1999
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
106
2007
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
90
2002
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
78
2007
Time-fractional diffusion of distributed order. Zbl 1229.35118
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
76
2008
Fractional calculus: Special functions and applications. Zbl 1030.26004
Mainardi, F.; Gorenflo, R.
73
2000
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
72
2004
The Wright functions as solutions of the time-fractional diffusion equation. Zbl 1053.35008
Mainardi, Francesco; Pagnini, Gianni
67
2003
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
64
2009
The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni
61
2010
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
51
2007
Fox \(H\) functions in fractional diffusion. Zbl 1061.33012
Mainardi, Francesco; Pagnini, Gianni; Saxena, R. K.
48
2005
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
47
2007
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002
Mainardi, 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 1303.26007
Mainardi, Francesco
46
2014
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
45
1998
Fractional diffusive waves. Zbl 1360.76272
Mainardi, Francesco; Paradisi, Paolo
45
2001
Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
44
1996
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
43
2007
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
42
2012
Models of dielectric relaxation based on completely monotone functions. Zbl 06663380
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
40
2016
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
39
1999
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
35
2010
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
35
1998
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.
33
2020
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
32
2010
The fractional Fick’s law for non-local transport processes. Zbl 0978.82080
Paradisi, P.; Cesari, R.; Mainardi, F.; Tampieri, F.
30
2001
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085
Mainardi, Francesco; Garrappa, Roberto
29
2015
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, 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 1381.35226
Luchko, Yuri; Mainardi, Francesco; Povstenko, Yuriy
28
2013
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
27
2003
On a special function arising in the time fractional diffusion-wave equation. Zbl 0921.33010
Mainardi, F.; Tomirotti, M.
27
1995
Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011
Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia
25
2015
Fractional relaxation with time-varying coefficient. Zbl 1305.26018
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni
25
2014
Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
21
2005
Fractional models of anomalous relaxation based on the Kilbas and Saigo function. Zbl 1307.34007
de Oliveira, Edmundo Capelas; Mainardi, Francesco; Vaz, Jayme jun.
20
2014
A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
19
2017
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco
19
2004
A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005
Mura, Antonio; Mainardi, Francesco
18
2009
Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082
Gorenflo, Rudolf; Mainardi, Francesco
18
2001
Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. Zbl 1050.33018
Mainardi, Francesco; Pagnini, Gianni
15
2003
Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
14
2007
On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
14
2017
A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023
Giusti, Andrea; Mainardi, Francesco
13
2016
Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
13
2007
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
12
2003
Asymptotic expansion for transient viscoelastic waves. Zbl 0351.73033
Buchen, Peter W.; Mainardi, Francesco
12
1975
Time fractional cable equation and applications in neurophysiology. Zbl 1374.92025
Vitali, 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 1351.26017
Tenreiro Machado, José António; Mainardi, Francesco; Kiryakova, Virginia; Atanacković, Teodor
11
2016
Fractional relaxation of distributed order. Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
10
2006
Applications of fractional calculus in mechanics. Zbl 1113.26303
Mainardi, Francesco
10
1998
The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco
10
2018
Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003
Mainardi, Francesco
8
2004
Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021
Gorenflo, R.; Mainardi, F.
8
1998
Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017
Mainardi, Francesco; Pagnini, Gianni
8
2008
Energy propagation in dissipative systems. I: Centrovelocity for linear systems. Zbl 0687.73036
Van Groesen, Embrecht; Mainardi, Francesco
8
1989
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
8
2004
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
7
2015
Evolution equations for the probabilistic generalization of the Voigt profile function. Zbl 1179.82008
Pagnini, Gianni; Mainardi, Francesco
7
2010
On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019
Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco
7
2017
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
7
2012
Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
6
2013
George William Scott Blair – the pioneer of fractional calculus in rheology. Zbl 1329.01079
Rogosin, Sergei; Mainardi, Francesco
6
2014
Scott-Blair models with time-varying viscosity. Zbl 1407.76007
Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco
6
2018
Variable-order fractional calculus: a change of perspective. Zbl 1471.26002
Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco
5
2021
Energy velocity for hyperbolic dispersive waves. Zbl 0605.73020
Mainardi, Francesco
5
1987
On Volterra functions and Ramanujan integrals. Zbl 1342.45001
Garrappa, Roberto; Mainardi, Francesco
5
2016
Balance laws and centro velocity in dissipative systems. Zbl 0728.73001
van Groesen, E.; Mainardi, F.
5
1990
The functions of the Wright type in fractional calculus. Zbl 1216.26004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni
5
2010
A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients. Zbl 06916883
Mainardi, Francesco
4
2018
Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Zbl 1260.60163
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
4
2012
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
4
2004
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1411.60052
Gorenflo, 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 1273.01048
Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei
4
2011
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
Signal velocity for transient waves in linear dissipative media. Zbl 0529.73027
Mainardi, Francesco
3
1983
Editorial. Fractional calculus: theory and applications. Zbl 1427.00050
3
2018
On transient waves in linear viscoelasticity. Zbl 07213199
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
3
2017
On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053
Mainardi, Francesco; Masina, Enrico
3
2018
On the evolution of fractional diffusive waves. Zbl 1469.35219
Consiglio, Armando; Mainardi, Francesco
2
2021
A representation theorem in the dynamic theory of porous media. Zbl 0288.73083
Boschi, E.; Mainardi, F.
2
1973
On shock-wave formation for blood flow in arteries. Zbl 0505.76140
Mainardi, F.; Buggisch, H.
2
1982
On the relation between sources and initial conditions for the wave and diffusion equations. Zbl 1409.35130
Carcione, José M.; Mainardi, Francesco
2
2017
On the asymptotics of Wright functions of the second kind. Zbl 1474.30015
Paris, Richard B.; Consiglio, Armando; Mainardi, Francesco
1
2021
Variable-order fractional calculus: a change of perspective. Zbl 1471.26002
Garrappa, Roberto; Giusti, Andrea; Mainardi, Francesco
5
2021
On the evolution of fractional diffusive waves. Zbl 1469.35219
Consiglio, Armando; Mainardi, Francesco
2
2021
On the asymptotics of Wright functions of the second kind. Zbl 1474.30015
Paris, Richard B.; Consiglio, Armando; Mainardi, Francesco
1
2021
Fractional diffusive waves in the Cauchy and signalling problems. Zbl 1472.35430
Consiglio, Armando; Mainardi, Francesco
1
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.
33
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
29
2020
The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco
10
2018
Scott-Blair models with time-varying viscosity. Zbl 1407.76007
Colombaro, 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 06916883
Mainardi, 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 1426.33053
Mainardi, Francesco; Masina, Enrico
3
2018
A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
19
2017
On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
14
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
7
2017
On transient waves in linear viscoelasticity. Zbl 07213199
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
3
2017
On the relation between sources and initial conditions for the wave and diffusion equations. Zbl 1409.35130
Carcione, José M.; Mainardi, Francesco
2
2017
Models of dielectric relaxation based on completely monotone functions. Zbl 06663380
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
40
2016
A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023
Giusti, 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 1351.26017
Tenreiro Machado, José António; Mainardi, Francesco; Kiryakova, Virginia; Atanacković, Teodor
11
2016
On Volterra functions and Ramanujan integrals. Zbl 1342.45001
Garrappa, Roberto; Mainardi, Francesco
5
2016
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085
Mainardi, Francesco; Garrappa, Roberto
29
2015
Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011
Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia
25
2015
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
7
2015
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, 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 1303.26007
Mainardi, Francesco
46
2014
Fractional relaxation with time-varying coefficient. Zbl 1305.26018
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni
25
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.
20
2014
George William Scott Blair – the pioneer of fractional calculus in rheology. Zbl 1329.01079
Rogosin, Sergei; Mainardi, Francesco
6
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
28
2013
Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
6
2013
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
42
2012
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
7
2012
Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Zbl 1260.60163
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
4
2012
Recent history of fractional calculus. Zbl 1221.26002
Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco
407
2011
Professor Rudolf Gorenflo and his contribution to fractional calculus. Zbl 1273.01048
Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei
4
2011
Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004
Mainardi, Francesco
825
2010
The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni
61
2010
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
35
2010
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
32
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
5
2010
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
64
2009
A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005
Mura, Antonio; Mainardi, Francesco
18
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
76
2008
Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017
Mainardi, Francesco; Pagnini, Gianni
8
2008
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
106
2007
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
78
2007
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
51
2007
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
47
2007
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002
Mainardi, Francesco; Pagnini, Gianni
47
2007
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
43
2007
Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
14
2007
Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
13
2007
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.
48
2005
Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
21
2005
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
72
2004
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco
19
2004
Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003
Mainardi, Francesco
8
2004
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
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
67
2003
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
27
2003
Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. Zbl 1050.33018
Mainardi, Francesco; Pagnini, Gianni
15
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
192
2002
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
157
2002
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
90
2002
Linear viscoelasticity. Zbl 1213.74076
Mainardi, Francesco
3
2002
The fundamental solutions of the time-fractional diffusion equation. Zbl 1068.35038
Mainardi, Francesco; Pagnini, Gianni
1
2002
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
344
2001
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
153
2001
Fractional diffusive waves. Zbl 1360.76272
Mainardi, Francesco; Paradisi, Paolo
45
2001
The fractional Fick’s law for non-local transport processes. Zbl 0978.82080
Paradisi, P.; Cesari, R.; Mainardi, F.; Tampieri, F.
30
2001
Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082
Gorenflo, 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 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
173
2000
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
128
2000
Fractional calculus: Special functions and applications. Zbl 1030.26004
Mainardi, F.; Gorenflo, R.
73
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
119
1999
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
39
1999
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
134
1998
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
45
1998
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
35
1998
Applications of fractional calculus in mechanics. Zbl 1113.26303
Mainardi, Francesco
10
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.
844
1997
Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010
Gorenflo, R.; Mainardi, F.
132
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
296
1996
The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036
Mainardi, F.
224
1996
Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
44
1996
On a special function arising in the time fractional diffusion-wave equation. Zbl 0921.33010
Mainardi, F.; Tomirotti, M.
27
1995
Dynamics of an impurity in a 1D periodic Burgers flow. Zbl 0841.76085
Angelucci, M. G.; Tampieri, F.; Mainardi, F.
1
1994
...and 8 more Documents
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
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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. Series B
16 Mathematical Methods in the Applied Sciences
16 Journal of Differential Equations
16 SIAM Journal on Scientific Computing
16 Inverse Problems in Science and Engineering
15 ZAMP. Zeitschrift für angewandte Mathematik und Physik
15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
15 Filomat
15 Mathematical Modelling of Natural Phenomena
14 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
14 Cybernetics and Systems Analysis
14 Lobachevskii Journal of Mathematics
14 Fractional Differential Calculus
13 Computer Methods in Applied Mechanics and Engineering
13 Turkish Journal of Mathematics
13 Nonlinear Analysis. Real World Applications
13 Journal of Nonlinear Science and Applications
12 Applicable Analysis
11 Journal of Vibration and Control
11 Differential Equations and Dynamical Systems
11 Journal of Evolution Equations
11 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
11 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
11 East Asian Journal on Applied Mathematics
10 Wave Motion
10 International Journal of Nonlinear Sciences and Numerical Simulation
10 Journal of Applied Mathematics
10 Mediterranean Journal of Mathematics
10 Axioms
10 Journal of Mathematics
9 International Journal of Engineering Science
9 Reports on Mathematical Physics
9 Journal of Functional Analysis
9 Stochastic Analysis and Applications
9 Numerical Methods for Partial Differential Equations
9 Journal of Mathematical Sciences (New York)
9 Discrete Dynamics in Nature and Society
9 Computational Methods in Applied Mathematics
9 Discrete and Continuous Dynamical Systems. Series S
9 Journal of Applied Nonlinear Dynamics
9 Vestnik KRAUNTS. Fiziko-Matematicheskie Nauki
8 Journal of Applied Probability
8 SIAM Journal on Numerical Analysis
8 Journal of Integral Equations and Applications
8 Advances in Computational Mathematics
8 Differential Equations
8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 Evolution Equations and Control Theory
8 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
7 Mathematics of Computation
7 Proceedings of the American Mathematical Society
7 Semigroup Forum
7 Mathematical and Computer Modelling
7 Complexity
7 International Journal of Applied Mathematics and Computer Science
7 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
7 Asian-European Journal of Mathematics
7 Advances in Applied Mathematics and Mechanics
7 Symmetry
...and 345 more Serials
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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)

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