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Mainardi, Francesco

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Author ID: mainardi.francesco Recent zbMATH articles by "Mainardi, Francesco"
Published as: Mainardi, F.; Mainardi, Francesco
External Links: Wikidata
Documents Indexed: 120 Publications since 1973, including 8 Books
Biographic References: 2 Publications

Publications by Year

Citations contained in zbMATH Open

103 Publications have been cited 5,482 times in 3,397 Documents Cited by Year
Fractals and fractional calculus in continuum mechanics. Zbl 0917.73004
Carpinteri, A.; Mainardi, F.
745
1997
Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004
Mainardi, Francesco
625
2010
Recent history of fractional calculus. Zbl 1221.26002
Tenreiro Machado, J.; Kiryakova, Virginia; Mainardi, Francesco
324
2011
The fundamental solution of the space-time fractional diffusion equation. Zbl 1054.35156
Mainardi, Francesco; Luchko, Yuri; Pagnini, Gianni
308
2001
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
290
2014
Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 1080.26505
Mainardi, Francesco
264
1996
The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036
Mainardi, F.
208
1996
Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033
Raberto, Marco; Scalas, Enrico; Mainardi, Francesco
154
2002
On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
153
2000
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
146
2001
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
137
2002
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
119
2000
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
115
2007
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
114
1998
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
105
2002
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
100
1999
Fractional calculus: Special functions and applications. Zbl 1030.26004
Mainardi, F.; Gorenflo, R.
81
2000
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
72
2004
Time-fractional diffusion of distributed order. Zbl 1229.35118
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
62
2008
The Wright functions as solutions of the time-fractional diffusion equation. Zbl 1053.35008
Mainardi, Francesco; Pagnini, Gianni
61
2003
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
59
2007
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
59
1998
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
58
2009
The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni
47
2010
Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
45
1996
Fox \(H\) functions in fractional diffusion. Zbl 1061.33012
Mainardi, Francesco; Pagnini, Gianni; Saxena, R. K.
44
2005
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
43
2007
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
40
2007
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
39
2012
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002
Mainardi, Francesco; Pagnini, Gianni
39
2007
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
37
1999
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
36
2014
Fractional diffusive waves. Zbl 1360.76272
Mainardi, Francesco; Paradisi, Paolo
36
2001
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
34
2010
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
33
2007
Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010
Gorenflo, R.; Mainardi, F.
32
1997
The fractional Fick’s law for non-local transport processes. Zbl 0978.82080
Paradisi, P.; Cesari, R.; Mainardi, F.; Tampieri, F.
30
2001
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
29
1998
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
28
2010
Models of dielectric relaxation based on completely monotone functions. Zbl 06663380
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
26
2016
On a special function arising in the time fractional diffusion-wave equation. Zbl 0921.33010
Mainardi, F.; Tomirotti, M.
26
1995
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
24
2003
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085
Mainardi, Francesco; Garrappa, Roberto
23
2015
Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011
Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia
22
2015
Renewal processes of Mittag-Leffler and Wright type. Zbl 1126.60070
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
21
2005
Fractional relaxation with time-varying coefficient. Zbl 1305.26018
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni
20
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
20
2013
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1125.76067
Gorenflo, Rudolf; Vivoli, Alessandro; Mainardi, Francesco
18
2004
A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005
Mura, Antonio; Mainardi, Francesco
17
2009
A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
16
2017
Fractional models of anomalous relaxation based on the Kilbas and Saigo function. Zbl 1307.34007
De Oliveira, Edmundo Capelas; Mainardi, Francesco; Vaz, Jayme jun.
16
2014
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
14
2003
Random walk models approximating symmetric space-fractional diffusion processes. Zbl 1007.60082
Gorenflo, Rudolf; Mainardi, Francesco
14
2001
On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
13
2017
Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
13
2007
Applications of fractional calculus in mechanics. Zbl 1113.26303
Mainardi, Francesco
10
1998
Asymptotic expansion for transient viscoelastic waves. Zbl 0351.73033
Buchen, Peter W.; Mainardi, Francesco
10
1975
Time fractional cable equation and applications in neurophysiology. Zbl 1374.92025
Vitali, Silvia; Castellani, Gastone; Mainardi, Francesco
9
2017
A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023
Giusti, Andrea; Mainardi, Francesco
9
2016
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
9
2003
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco
8
2020
Fractional relaxation of distributed order. Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
8
2006
Signalling problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations. Zbl 0932.35021
Gorenflo, R.; Mainardi, F.
8
1998
Energy propagation in dissipative systems. I: Centrovelocity for linear systems. Zbl 0687.73036
Van Groesen, Embrecht; Mainardi, Francesco
8
1989
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
7
2016
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
7
2004
Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003
Mainardi, Francesco
7
2004
George William Scott Blair – the pioneer of fractional calculus in rheology. Zbl 1329.01079
Rogosin, Sergei; Mainardi, Francesco
6
2014
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
6
2012
Evolution equations for the probabilistic generalization of the Voigt profile function. Zbl 1179.82008
Pagnini, Gianni; Mainardi, Francesco
6
2010
Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017
Mainardi, Francesco; Pagnini, Gianni
6
2008
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
6
2004
The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco
5
2018
On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019
Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco
5
2017
Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
5
2013
Professor Rudolf Gorenflo and his contribution to fractional calculus. Zbl 1273.01048
Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei
5
2011
Balance laws and centro velocity in dissipative systems. Zbl 0728.73001
van Groesen, E.; Mainardi, F.
5
1990
On Volterra functions and Ramanujan integrals. Zbl 1342.45001
Garrappa, Roberto; Mainardi, Francesco
4
2016
Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion. Zbl 1260.60163
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
4
2012
Discrete and continuous random walk models for space-time fractional diffusion. Zbl 1411.60052
Gorenflo, R.; Vivoli, A.; Mainardi, F.
4
2006
Energy velocity for hyperbolic dispersive waves. Zbl 0605.73020
Mainardi, Francesco
4
1987
Wave propagation in viscoelastic media. Euromech Colloquium 127 ”Wave propagation in viscoelastic media”, held at Taormina, Sicily, Italy, in April 1980. Zbl 0493.73028
Mainardi, F. (ed.)
4
1982
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.
3
2020
A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients. Zbl 06916883
Mainardi, Francesco
3
2018
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
3
2015
The functions of the Wright type in fractional calculus. Zbl 1216.26004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni
3
2010
Mellin convolution for subordinated stable processes. Zbl 1411.60026
Mainardi, F.; Pagnini, G.; Gorenflo, R.
3
2006
Linear viscoelasticity. Zbl 1213.74076
Mainardi, Francesco
3
2002
Signal velocity for transient waves in linear dissipative media. Zbl 0529.73027
Mainardi, Francesco
3
1983
Scott-Blair models with time-varying viscosity. Zbl 1407.76007
Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco
2
2018
On shock-wave formation for blood flow in arteries. Zbl 0505.76140
Mainardi, F.; Buggisch, H.
2
1982
A representation theorem in the dynamic theory of porous media. Zbl 0288.73083
Boschi, E.; Mainardi, F.
2
1973
On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053
Mainardi, Francesco; Masina, Enrico
1
2019
Editorial. Fractional calculus: theory and applications. Zbl 1427.00050
Mainardi, Francesco (ed.)
1
2018
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
The fundamental solutions of the time-fractional diffusion equation. Zbl 1068.35038
Mainardi, Francesco; Pagnini, Gianni
1
2002
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
Guran, Ardéshir (ed.); De Hoop, Adrianus (ed.); Guicking, Dieter (ed.); Mainardi, Francesco (ed.)
1
2001
On linear differential equations of fractional order. Zbl 0919.34010
Mainardi, Francesco
1
1997
A practical guide to Prabhakar fractional calculus. Zbl 1437.33019
Giusti, Andrea; Colombaro, Ivano; Garra, Roberto; Garrappa, Roberto; Polito, Federico; Popolizio, Marina; Mainardi, Francesco
8
2020
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.
3
2020
On modifications of the exponential integral with the Mittag-Leffler function. Zbl 1426.33053
Mainardi, Francesco; Masina, Enrico
1
2019
The fractional Dodson diffusion equation: a new approach. Zbl 1403.35314
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco
5
2018
A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients. Zbl 06916883
Mainardi, Francesco
3
2018
Scott-Blair models with time-varying viscosity. Zbl 1407.76007
Colombaro, Ivano; Garra, Roberto; Giusti, Andrea; Mainardi, Francesco
2
2018
Editorial. Fractional calculus: theory and applications. Zbl 1427.00050
Mainardi, Francesco (ed.)
1
2018
A class of linear viscoelastic models based on Bessel functions. Zbl 1383.74019
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
16
2017
On the propagation of transient waves in a viscoelastic Bessel medium. Zbl 1370.74028
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
13
2017
Time fractional cable equation and applications in neurophysiology. Zbl 1374.92025
Vitali, Silvia; Castellani, Gastone; Mainardi, Francesco
9
2017
On a generalized three-parameter Wright function of Le Roy type. Zbl 1374.33019
Garrappa, Roberto; Rogosin, Sergei; Mainardi, Francesco
5
2017
Models of dielectric relaxation based on completely monotone functions. Zbl 06663380
Garrappa, Roberto; Mainardi, Francesco; Guido, Maione
26
2016
A dynamic viscoelastic analogy for fluid-filled elastic tubes. Zbl 1348.76023
Giusti, Andrea; Mainardi, Francesco
9
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
7
2016
On Volterra functions and Ramanujan integrals. Zbl 1342.45001
Garrappa, Roberto; Mainardi, Francesco
4
2016
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. Zbl 1349.65085
Mainardi, Francesco; Garrappa, Roberto
23
2015
Fractional calculus: quo vadimus? (where are we going?). Zbl 1309.26011
Tenreiro Machado, J.; Mainardi, Francesco; Kiryakova, Virginia
22
2015
On the fractional Poisson process and the discretized stable subordinator. Zbl 1415.60051
Gorenflo, Rudolf; Mainardi, Francesco
3
2015
Mittag-Leffler functions, related topics and applications. Zbl 1309.33001
Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei V.
290
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
36
2014
Fractional relaxation with time-varying coefficient. Zbl 1305.26018
Garra, Roberto; Giusti, Andrea; Mainardi, Francesco; Pagnini, Gianni
20
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.
16
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
20
2013
Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes. Zbl 1339.60116
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
5
2013
An historical perspective on fractional calculus in linear viscoelasticity. Zbl 1314.74005
Mainardi, Francesco
39
2012
Parametric subordination in fractional diffusion processes. Zbl 1371.60135
Gorenflo, Rudolf; Mainardi, Francesco
6
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
324
2011
Professor Rudolf Gorenflo and his contribution to fractional calculus. Zbl 1273.01048
Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei
5
2011
Fractional calculus and waves in linear viscoelasticity. An introduction to mathematical models. Zbl 1210.26004
Mainardi, Francesco
625
2010
The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey. Zbl 1222.60060
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni
47
2010
A poster about the recent history of fractional calculus. Zbl 1221.26013
Tenreiro-Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
34
2010
A poster about the old history of fractional calculus. Zbl 1222.26015
Tenreiro Machado, J. A.; Kiryakova, Virginia; Mainardi, Francesco
28
2010
Evolution equations for the probabilistic generalization of the Voigt profile function. Zbl 1179.82008
Pagnini, Gianni; Mainardi, Francesco
6
2010
The functions of the Wright type in fractional calculus. Zbl 1216.26004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni
3
2010
Some recent advances in theory and simulation of fractional diffusion processes. Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
58
2009
A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Zbl 1173.26005
Mura, Antonio; Mainardi, Francesco
17
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
62
2008
Mellin-Barnes integrals for stable distributions and their convolutions. Zbl 1175.26017
Mainardi, Francesco; Pagnini, Gianni
6
2008
A new dissipation model based on memory mechanism. Zbl 1213.74005
Caputo, M.; Mainardi, F.
115
2007
Some aspects of fractional diffusion equations of single and distributed order. Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
59
2007
Continuous-time random walk and parametric subordination in fractional diffusion. Zbl 1142.82363
Gorenflo, Rudolf; Mainardi, Francesco; Vivoli, Alessandro
43
2007
Time-fractional derivatives in relaxation processes: a tutorial survey. Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
40
2007
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Zbl 1120.35002
Mainardi, Francesco; Pagnini, Gianni
39
2007
The two forms of fractional relaxation of distributed order. Zbl 1165.26302
Mainardi, Francesco; Mura, Antonio; Gorenfloh, Rudolf; Stojanović, Mirjana
33
2007
Sub-diffusion equations of fractional order and their fundamental solutions. Zbl 1135.35004
Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni; Gorenflo, Rudolf
16
2007
Beyond the Poisson renewal process: a tutorial survey. Zbl 1115.60082
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro
13
2007
Fractional relaxation of distributed order. Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
8
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.
44
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
18
2004
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
7
2004
Applications of integral transforms in fractional diffusion processes. Zbl 1093.45003
Mainardi, Francesco
7
2004
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
6
2004
The Wright functions as solutions of the time-fractional diffusion equation. Zbl 1053.35008
Mainardi, Francesco; Pagnini, Gianni
61
2003
Mellin transform and subordination laws in fractional diffusion processes. Zbl 1083.60032
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
24
2003
Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. Zbl 1050.33018
Mainardi, Francesco; Pagnini, Gianni
14
2003
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
9
2003
Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033
Raberto, Marco; Scalas, Enrico; Mainardi, Francesco
154
2002
Time fractional diffusion: A discrete random walk approach. Zbl 1009.82016
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Paradisi, Paolo
137
2002
Fractional diffusion: probability distributions and random walk models. Zbl 0986.82037
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
105
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
308
2001
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
146
2001
Fractional diffusive waves. Zbl 1360.76272
Mainardi, Francesco; Paradisi, Paolo
36
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
14
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
Guran, Ardéshir (ed.); De Hoop, Adrianus (ed.); Guicking, Dieter (ed.); Mainardi, Francesco (ed.)
1
2001
On Mittag-Leffler-type functions in fractional evolution processes. Zbl 0970.45005
Mainardi, Francesco; Gorenflo, Rudolf
153
2000
Wright functions as scale-invariant solutions of the diffusion-wave equation. Zbl 0973.35012
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
119
2000
Fractional calculus: Special functions and applications. Zbl 1030.26004
Mainardi, F.; Gorenflo, R.
81
2000
Analytical properties and applications of the Wright function. Zbl 1027.33006
Gorenflo, Rudolf; Luchko, Yuri; Mainardi, Francesco
100
1999
Approximation of Lévy-Feller diffusion by random walk. Zbl 0948.60006
Gorenflo, R.; Mainardi, F.
37
1999
Random walk models for space-fractional diffusion processes. Zbl 0946.60039
Gorenflo, R.; Mainardi, F.
114
1998
Fractional calculus and stable probability distributions. Zbl 0934.35008
Gorenflo, R.; Mainardi, F.
59
1998
Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena. Zbl 0921.33009
Gorenflo, Rudolf; Mainardi, Francesco; Srivastava, Hari M.
29
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.
745
1997
Fractional calculus: integral and differential equations of fractional order. Zbl 1438.26010
Gorenflo, R.; Mainardi, F.
32
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
264
1996
The fundamental solutions for the fractional diffusion-wave equation. Zbl 0879.35036
Mainardi, F.
208
1996
Fractional oscillations and Mittag-Leffler functions. Zbl 0916.34011
Gorenflo, R.; Mainardi, F.
45
1996
On a special function arising in the time fractional diffusion-wave equation. Zbl 0921.33010
Mainardi, F.; Tomirotti, M.
26
1995
Dynamics of an impurity in a 1D periodic Burgers flow. Zbl 0841.76085
Angelucci, M. G.; Tampieri, F.; Mainardi, F.
1
1994
Energy propagation in linear hyperbolic systems in the presence of dissipation. Zbl 0921.35087
Mainardi, Francesco; Tocci, Donatella
1
1993
Balance laws and centro velocity in dissipative systems. Zbl 0728.73001
van Groesen, E.; Mainardi, F.
5
1990
Energy propagation in dissipative systems. I: Centrovelocity for linear systems. Zbl 0687.73036
Van Groesen, Embrecht; Mainardi, Francesco
8
1989
Energy velocity for hyperbolic dispersive waves. Zbl 0605.73020
Mainardi, Francesco
4
1987
Signal velocity for transient waves in linear dissipative media. Zbl 0529.73027
Mainardi, Francesco
3
1983
Wave propagation in viscoelastic media. Euromech Colloquium 127 ”Wave propagation in viscoelastic media”, held at Taormina, Sicily, Italy, in April 1980. Zbl 0493.73028
Mainardi, F. (ed.)
4
1982
On shock-wave formation for blood flow in arteries. Zbl 0505.76140
Mainardi, F.; Buggisch, H.
2
1982
...and 3 more Documents
all top 5

Cited by 4,015 Authors

112 Băleanu, Dumitru I.
65 Machado, José António Tenreiro
61 Mainardi, Francesco
58 Liu, Fawang
48 Momani, Shaher M.
47 Tarasov, Vasily E.
33 Anh, Vo V.
32 Chen, Yangquan
30 Povstenko, Yuriy Z.
30 Turner, Ian William
28 Meerschaert, Mark M.
28 Odibat, Zaid M.
24 Gorenflo, Rudolf
24 Sun, Zhizhong
23 de Oliveira, Edmundo Capelas
23 Trujillo, Juan J.
22 Abdeljawad, Thabet
22 Atanackovic, Teodor M.
22 Luchko, Yuri
22 Pagnini, Gianni
20 Leonenko, Nikolai N.
20 Wang, Jinrong
19 Agarwal, Ravi P.
18 Deng, Weihua
18 Garrappa, Roberto
18 Li, Changpin
18 Polito, Federico
18 Wang, Hong
17 Al-saedi, Ahmed Eid Salem
17 Lizama, Carlos
17 Saxena, Ram Kishore
16 Ahmad, Bashir
16 Beghin, Luisa
16 Chen, Wen
16 Dehghan Takht Fooladi, Mehdi
16 Garra, Roberto
16 Karniadakis, George Em
16 Mathai, Arakaparampli Mathai
16 Pilipović, Stevan
16 Sandev, Trifce
15 Atangana, Abdon
15 Bhalekar, Sachin
15 Giusti, Andrea
15 Jafari, Hossein
15 Tang, Yifa
15 Tomovski, Živorad
15 Warma, Mahamadi
15 Zorica, Dusan
14 Lopes, António M.
14 Nieto Roig, Juan Jose
14 Srivastava, Hari Mohan
14 Sun, Hongguang
14 Torres, Delfim Fernando Marado
14 Wei, Ting
14 Yang, Xiao-Jun
13 Ansari, Alireza
13 Benchohra, Mouffak
13 Bhrawy, Ali Hassan
13 Jarad, Fahd
13 Kiryakova, Virginia S.
13 Liu, Yuji
13 Zaky, Mahmoud A.
12 Daftardar-Gejji, Varsha
12 Duan, Junsheng
12 Luchko, Yurii F.
12 Nguyen Huy Tuan
12 Ordokhani, Yadollah
12 Yamamoto, Masahiro
11 Abbaszadeh, Mostafa
11 Agrawal, Om Prakash
11 Arqub, Omar Abu
11 Ford, Neville J.
11 Ge, Fudong
11 Jiang, Xiaoyun
11 Liu, Wenbin
11 Muslih, Sami I.
11 Ntouyas, Sotiris K.
11 Pandey, Dwijendra Narain
11 Scalas, Enrico
11 Sun, Haiwei
11 Zayernouri, Mohsen
11 Zhou, Yong
10 Balachandran, Krishnan
10 Bazhlekova, Emilia G.
10 Bulavatskyĭ, Volodymyr M.
10 Burrage, Kevin
10 Gómez-Aguilar, José Francisco
10 Kaminski Lenzi, Ervin
10 Kiliçman, Adem
10 Konjik, Sanja
10 Orsingher, Enzo
10 Peng, Jigen
10 Ponce, Rodrigo F.
10 Umarov, Sabir R.
10 Vanterler da Costa Sousa, José
10 Wang, Yuanming
9 Agarwal, Praveen
9 Babolian, Esmail
9 Bäumer, Boris
9 da Silva, José Luís
...and 3,915 more Authors
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Cited in 410 Serials

250 Fractional Calculus & Applied Analysis
170 Applied Mathematics and Computation
158 Computers & Mathematics with Applications
105 Journal of Computational and Applied Mathematics
103 Communications in Nonlinear Science and Numerical Simulation
103 Advances in Difference Equations
95 Chaos, Solitons and Fractals
86 Journal of Computational Physics
86 Nonlinear Dynamics
82 Abstract and Applied Analysis
57 Journal of Mathematical Analysis and Applications
56 Journal of Mathematical Physics
54 Applied Mathematical Modelling
50 Applied Numerical Mathematics
46 Computational and Applied Mathematics
43 Mathematical Problems in Engineering
37 Journal of Scientific Computing
34 Numerical Algorithms
33 Applied Mathematics Letters
30 Advances in Mathematical Physics
29 Mathematical Methods in the Applied Sciences
29 Integral Transforms and Special Functions
28 Physica A
28 Journal of Applied Mathematics and Computing
28 Mathematics
25 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
24 Chaos
24 International Journal of Differential Equations
23 International Journal of Applied and Computational Mathematics
22 Meccanica
22 Boundary Value Problems
20 Engineering Analysis with Boundary Elements
19 Journal of Statistical Physics
18 Acta Mechanica
18 International Journal of Theoretical Physics
17 SIAM Journal on Scientific Computing
16 Journal of Differential Equations
16 Nonlinear Analysis. Real World Applications
16 Journal of Applied Mathematics
16 Fractional Differential Calculus
15 Computer Methods in Applied Mechanics and Engineering
15 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
15 Journal of Vibration and Control
15 Mediterranean Journal of Mathematics
15 Mathematical Modelling of Natural Phenomena
15 Journal of Nonlinear Science and Applications
14 Mathematics and Computers in Simulation
14 Stochastic Processes and their Applications
13 Physics Letters. A
13 Statistics & Probability Letters
13 Numerical Methods for Partial Differential Equations
13 International Journal of Computer Mathematics
12 ZAMP. Zeitschrift für angewandte Mathematik und Physik
12 Differential Equations and Dynamical Systems
12 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
11 Applicable Analysis
11 Inverse Problems
11 Journal of the Franklin Institute
11 Cybernetics and Systems Analysis
11 Discrete and Continuous Dynamical Systems. Series B
11 Inverse Problems in Science and Engineering
11 Journal of Function Spaces
10 International Journal of Engineering Science
10 Wave Motion
10 Journal of Integral Equations and Applications
10 Discrete Dynamics in Nature and Society
10 International Journal of Nonlinear Sciences and Numerical Simulation
10 Axioms
10 East Asian Journal on Applied Mathematics
9 Stochastic Analysis and Applications
9 Complexity
9 Differential Equations
9 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
8 SIAM Journal on Numerical Analysis
8 Journal of Inequalities and Applications
8 Journal of Evolution Equations
8 Asian-European Journal of Mathematics
8 Asian Journal of Control
8 Vestnik KRAUNTS. Fiziko-Matematicheskie Nauki
7 Journal of Applied Probability
7 Journal of Functional Analysis
7 Journal of Optimization Theory and Applications
7 Semigroup Forum
7 Mathematical and Computer Modelling
7 Journal of Mathematical Sciences (New York)
7 Fractals
7 Mathematics and Mechanics of Solids
7 Computational Methods in Applied Mathematics
7 Symmetry
6 International Journal of Modern Physics B
6 Reports on Mathematical Physics
6 Mathematics of Computation
6 Automatica
6 Acta Applicandae Mathematicae
6 Annals of Physics
6 Continuum Mechanics and Thermodynamics
6 Journal of the Egyptian Mathematical Society
6 Journal of Inverse and Ill-Posed Problems
6 Advances in Computational Mathematics
6 International Journal of Applied Mathematics and Computer Science
...and 310 more Serials
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Cited in 53 Fields

1,402 Partial differential equations (35-XX)
1,056 Real functions (26-XX)
1,021 Numerical analysis (65-XX)
966 Ordinary differential equations (34-XX)
354 Special functions (33-XX)
348 Probability theory and stochastic processes (60-XX)
340 Integral equations (45-XX)
238 Operator theory (47-XX)
221 Mechanics of deformable solids (74-XX)
191 Systems theory; control (93-XX)
150 Fluid mechanics (76-XX)
117 Integral transforms, operational calculus (44-XX)
113 Statistical mechanics, structure of matter (82-XX)
109 Biology and other natural sciences (92-XX)
98 Calculus of variations and optimal control; optimization (49-XX)
91 Dynamical systems and ergodic theory (37-XX)
74 Classical thermodynamics, heat transfer (80-XX)
65 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
59 Quantum theory (81-XX)
58 Approximations and expansions (41-XX)
49 Mechanics of particles and systems (70-XX)
42 Information and communication theory, circuits (94-XX)
38 Harmonic analysis on Euclidean spaces (42-XX)
38 Functional analysis (46-XX)
38 Statistics (62-XX)
37 Functions of a complex variable (30-XX)
27 Difference and functional equations (39-XX)
26 Optics, electromagnetic theory (78-XX)
25 Measure and integration (28-XX)
22 Global analysis, analysis on manifolds (58-XX)
21 Linear and multilinear algebra; matrix theory (15-XX)
21 Computer science (68-XX)
20 Operations research, mathematical programming (90-XX)
19 Geophysics (86-XX)
14 Number theory (11-XX)
13 Combinatorics (05-XX)
13 Relativity and gravitational theory (83-XX)
11 Abstract harmonic analysis (43-XX)
10 History and biography (01-XX)
10 Sequences, series, summability (40-XX)
6 General and overarching topics; collections (00-XX)
6 Several complex variables and analytic spaces (32-XX)
6 Differential geometry (53-XX)
4 Potential theory (31-XX)
3 Mathematics education (97-XX)
2 Algebraic geometry (14-XX)
2 General topology (54-XX)
1 Field theory and polynomials (12-XX)
1 Commutative algebra (13-XX)
1 Group theory and generalizations (20-XX)
1 Convex and discrete geometry (52-XX)
1 Algebraic topology (55-XX)
1 Manifolds and cell complexes (57-XX)

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