Francesco Mainardi

Q: What Schools Are Affiliated With Francesco Mainardi

Francesco Mainardi is affiliated with the following schools: University of Sydney, Indian Institute of Science, University of Bologna

Francesco Mainardi's AcademicInfluence.com Rankings

Francesco Mainardi

Physics

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#4839

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Physics

Francesco Mainardi's Degrees

PhD Physics University of Bologna

Why Is Francesco Mainardi Influential?

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According to Wikipedia, Francesco Mainardi is an Italian physicist and mathematician. Early life Mainardi was born in Lugo, Italy, on December 29, 1942. He graduated from the University of Bologna in 1966 with a degree in theoretical physics.

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Francesco Mainardi's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Fractional Calculus (2018) (1726)
Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models (2010) (1700)
Fractals and fractional calculus in continuum mechanics (1997) (1465)
Fractional Calculus: Integral and Differential Equations of Fractional Order (2008) (1449)
Recent history of fractional calculus (2011) (1305)
Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics (2012) (1210)
Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena (1996) (939)
Mittag-Leffler Functions, Related Topics and Applications (2014) (871)
The fundamental solution of the space-time fractional diffusion equation (2007) (806)
Fractional calculus and continuous-time finance (2000) (784)
Multi-index Mittag-Leffler Functions (2014) (740)
Linear models of dissipation in anelastic solids (1971) (710)
A new dissipation model based on memory mechanism (1971) (710)
The fundamental solutions for the fractional diffusion-wave equation (1996) (610)
On Mittag-Leffler-type functions in fractional evolution processes (2000) (537)
Waiting-times and returns in high-frequency financial data: an empirical study (2002) (495)
Fractional calculus and continuous-time finance II: the waiting-time distribution (2000) (495)
Creep, relaxation and viscosity properties for basic fractional models in rheology (2011) (395)
Time Fractional Diffusion: A Discrete Random Walk Approach (2002) (363)
Discrete random walk models for space-time fractional diffusion (2002) (288)
Fractional Calculus and Continuous-Time Finance III : the Diffusion Limit (2001) (276)
Analytical properties and applications of the Wright function (2007) (264)
Wright functions as scale-invariant solutions of the diffusion-wave equation (2000) (260)
Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation. (2004) (197)
Time-fractional derivatives in relaxation processes: a tutorial survey (2008) (197)
A fractional generalization of the Poisson processes (2007) (190)
Time-fractional Diffusion of Distributed Order (2007) (185)
Fox H functions in fractional diffusion (2005) (179)
The Wright functions as solutions of the time-fractional diffusion equation (2003) (177)
Some aspects of fractional diffusion equations of single and distributed order (2007) (173)
The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey (2010) (172)
Probability distributions generated by fractional diffusion equations (2007) (159)
Continuous-time random walk and parametric subordination in fractional diffusion (2007) (157)
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics (2011) (146)
Time-domain Modeling of Constant-Q Seismic Waves Using Fractional Derivatives (2002) (145)
The fractional Fick's law for non-local transport processes (2001) (141)
An historical perspective on fractional calculus in linear viscoelasticity (2010) (135)
Fractional calculus and stable probability distributions (1998) (132)
Some recent advances in theory and simulation of fractional diffusion processes (2007) (132)
Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk (2007) (126)
Models of dielectric relaxation based on completely monotone functions (2016) (125)
The Fractional Langevin Equation: Brownian Motion Revisited (2008) (117)
Fractional Diffusive Waves (2001) (113)
The Two Forms of Fractional Relaxation of Distributed Order (2007) (113)
Probability distributions generated by fractional diffusion equations 1 (2007) (111)
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order (2007) (109)
A practical guide to Prabhakar fractional calculus (2020) (99)
ON SOME PROPERTIES OF THE MITTAG-LEFFLER FUNCTION E α ( − t α ) , COMPLETELY MONOTONE FOR t > 0 WITH 0 < α < 1 (2014) (98)
The time fractional diffusion-wave equation (1995) (96)
A Poster about the Recent History of Fractional Calculus (2010) (93)
Anomalous waiting times in high-frequency financial data (2003) (90)
Approximation of Levy-Feller Diffusion by Random Walk (1999) (89)
Fractional diffusion: probability distributions and random walk models (2002) (87)
On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$ (2013) (86)
Seismic pulse propagation with constant Q and stable probability distributions (1997) (84)
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics (2015) (82)
Essentials of Fractional Calculus (2010) (82)
A Poster about the Old History of Fractional Calculus (2010) (78)
Random walk models approximating symmetric space-fractional diffusion processes (2012) (76)
Mellin transform and subordination laws in fractional diffusion processes (2007) (75)
Fractional relaxation in anelastic solids (1994) (75)
Non-Markovian diffusion equations and processes: Analysis and simulations (2007) (68)
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015) (65)
Beyond the Poisson renewal process: A tutorial survey (2007) (65)
Fractional Oscillations And Mittag-Leffler Functions (1996) (64)
A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics (2007) (63)
Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects (2007) (61)
Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation (2012) (60)
Renewal processes of Mittag-Leffler and Wright type (2007) (58)
Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals (2003) (55)
Fractional relaxation with time-varying coefficient (2014) (52)
Fractional Calculus: Theory and Applications (2018) (51)
Simply and multiply scaled diffusion limits for continuous time random walks (2005) (50)
Fractional models of anomalous relaxation based on the Kilbas and Saigo function (2014) (50)
Discrete and Continuous Random Walk Models for Space-Time Fractional Diffusion (2004) (50)
A model of diffusive waves in viscoelasticity based on fractional calculus (1997) (49)
REVISITING THE DERIVATION OF THE FRACTIONAL DIFFUSION EQUATION (2002) (48)
Sub-diffusion equations of fractional order and their fundamental solutions (2007) (45)
George William Scott Blair – the pioneer of fractional calculus in rheology (2014) (44)
A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus (2017) (41)
Subordination pathways to fractional diffusion (2011) (41)
A dynamic viscoelastic analogy for fluid-filled elastic tubes (2015) (40)
Why the Mittag-Leffler Function Can Be Considered the Queen Function of the Fractional Calculus? (2020) (40)
A class of linear viscoelastic models based on Bessel functions (2016) (38)
Cauchy and Signaling Problems for the Time-Fractional Diffusion-Wave Equation (2014) (37)
The origin of infinitely divisible distributions: from de Finetti's problem to Levy-Khintchine formula (2008) (33)
Variable-order fractional calculus: A change of perspective (2021) (33)
Some properties of the fundamental solution to the signalling problem for the fractional diffusion-wave equation (2013) (33)
On the propagation of transient waves in a viscoelastic Bessel medium (2016) (32)
The fractional Dodson diffusion equation: a new approach (2017) (31)
Parametric subordination in fractional diffusion processes (2012) (31)
The viscous damping of capillary — Gravity waves (1987) (30)
Parametric subordination in fractional diffusion processes 1 (2012) (29)
On the Fractional Poisson Process and the Discretized Stable Subordinator (2013) (28)
Integral and Differential Equations of Fractional Order Integral and Differential Equations of Fractional Order (28)
On transient waves in linear viscoelasticity (2017) (27)
Evolution equations for the probabilistic generalization of the Voigt profile function (2007) (27)
On infinite series concerning zeros of Bessel functions of the first kind (2016) (25)
The Wright Functions of the Second Kind in Mathematical Physics (2020) (25)
The Classical Mittag-Leffler Function (2020) (25)
A generalized Fick's law to describe non-local transport effects (2001) (25)
Energy velocity for hyperbolic dispersive waves (1987) (24)
Mittag-Leffler function: properties and applications (2019) (24)
Time Fractional Cable Equation And Applications in Neurophysiology (2017) (23)
Speculative option valuation and the fractional diffusion equation (2005) (23)
On a general class of constant-Q solids (1982) (22)
Scott-Blair models with time-varying viscosity (2018) (22)
FRACTIONAL RELAXATION OF DISTRIBUTED ORDER (2006) (21)
Energy propagation in dissipative systems Part I: Centrovelocity for linear systems (1989) (21)
Discrete and Continuous Random Walk Models for Space-Time Fractional Diffusion (2006) (20)
On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep (2011) (19)
Mellin-Barnes integrals for stable distributions and their convolutions (2008) (19)
Applications of integral transforms in fractional diffusion processes (2004) (19)
Laplace-Laplace analysis of the fractional Poisson process (2013) (19)
On a generalized three-parameter wright function of Le Roy type (2017) (18)
Generalized Fractional Master Equation for Self-Similar Stochastic Processes Modelling Anomalous Diffusion (2012) (17)
Soil amplification of plane seismic waves (1980) (16)
A Note on the Equivalence of Fractional Relaxation Equations to Differential Equations with Varying Coefficients (2017) (16)
Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes (2013) (16)
Fractional Diffusion in Finance : Basic Theory (2001) (15)
On the Intertrade Waiting-time Distribution (2005) (15)
THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION (2001) (13)
FRACTIONAL RELAXATION AND TIME-FRACTIONAL DIFFUSION OF DISTRIBUTED ORDER (2006) (13)
the pioneer of the Mellin-Barnes integrals (2007) (13)
Fractional Viscoelastic Models (2010) (13)
Balance laws and centro velocity in dissipative systems (1989) (13)
Pressure pulses in fluid filled distensible tubes (1985) (12)
Wave Propagation in Viscoelastic Media (1983) (11)
A generalization of the Becker model in linear viscoelasticity: creep, relaxation and internal friction (2017) (11)
On Volterra functions and Ramanujan integrals (2016) (11)
On the Advent of Fractional Calculus in Econophysics via Continuous-Time Random Walk (2020) (11)
Wave front expansions for transient viscoelastic waves (1975) (10)
The fundamental solutions of the time-fractional diffusion equation (2002) (10)
The legacy of A.Ya. Khintchine's work in probability theory (2017) (10)
Professor Rudolf Gorenflo and his contribution to fractional calculus (2011) (10)
Fractional diffusion-wave phenomena (2019) (10)
Energy propagation in linear hyperbolic systems (1989) (9)
CONTINUOUS TIME RANDOM WALK AND TIME FRACTIONAL DIFFUSION: A NUMERICAL COMPARISON BETWEEN THE FUNDAMENTAL SOLUTIONS (2005) (9)
Signal velocity for transient waves in linear dissipative media (1983) (9)
Brownian motion and anomalous diffusion revisited via a fractional Langevin equation (2010) (9)
A Tutorial on the Basic Special Functions of Fractional Calculus (2020) (9)
On signal velocity for anomalous dispersive waves (1983) (9)
The function of the Wright type in fractional calculus (2010) (9)
for anomalous relaxation in dielectrics (2011) (9)
On the evolution of fractional diffusive waves (2019) (8)
Fractional relaxation-oscillation phenomena (2019) (8)
On energy velocity of viscoelastic waves (1973) (8)
A one parameter class of fractional Maxwell-like models (2016) (8)
The Mittag-Leffler function in the thinning theory for renewal processes (2018) (7)
Power laws, random walks, and fractional diffusion processes as well scaled refinement limits (2005) (7)
Thermoelasticity and P-wave simulation based on the Cole-Cole model (2020) (7)
Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s-μ exp(-sν) (2020) (7)
Fractional Calculus in Wave Propagation Problems (2012) (7)
Brownian motion and anomalous diffusion revisited via a fractional Langevin equation 1 (2010) (6)
Fractional calculus and the Schrödinger equation (2006) (6)
SPACE-TIME FRACTIONAL DIFFUSION: EXACT SOLUTIONS AND PROBABILITY INTERPRETATION (2002) (6)
a Proposal to Search for Leptonic Quarks and Heavy Leptons Produced by Adone (1995) (6)
On modifications of the exponential integral with the Mittag-Leffler function (2018) (6)
Becker and Lomnitz rheological models: a comparison (2012) (6)
Learning short-option valuation in the presence of rare events (2000) (6)
Wave Dispersion in the Linearised Fractional Korteweg - de Vries equation (2017) (6)
A Representation Theorem in the Dynamic Theory of Porous Media (1973) (5)
Tricomi's Method for the Laplace Transform and Orthogonal Polynomials (2021) (5)
On energy propagation for internal waves in dissipative fluids (1992) (5)
A renewal process of Mittag-Leffler type (2004) (5)
Wright functions of the second kind and Whittaker functions (2021) (5)
On Nonlinear Waves in Liquid-Filled Elastic Tubes (1983) (5)
Acoustic Interactions with Submerged Elastic Structures (2004) (4)
On Linear Dispersive Waves With Dissipation (1984) (4)
The waiting-time distribution of LIFFE bond futures (2000) (4)
International Centre for Mechanical Sciences Palazzo del Torso, Piazza Garibaldi, Udine, Italy FRACTIONAL CALCULUS : Some Basic Problems in Continuum and Statistical Mechanics (2012) (4)
On the relation between sources and initial conditions for the wave and diffusion equations (2017) (4)
Improving Pose Estimation Using Image, Sensor and Model Uncertainty (1994) (3)
Fractional cable model for signal conduction in spiny neuronal dendrites (2017) (3)
Applications to Fractional Order Equations (2020) (3)
Special Section: Fractional Calculus in Vibration and Acoustics (2014) (3)
Differentiation of the Wright Functions with Respect to Parameters and Other Results (2020) (3)
Energy Propagation in Linear Hyperbolic Systems in the Presence of Dissipation (1993) (3)
Dissipative effects on internal gravity waves in geophysical fluids (1991) (3)
Positivity constraints and approximation methods in linear viscoelasticity (1979) (3)
The Two-Parametric Mittag-Leffler Function (2020) (3)
Fractional Diffusive Waves in the Cauchy and Signalling Problems (2021) (3)
Emergence of Fractional Kinetics in Spiny Dendrites (2018) (3)
Essentials of Linear Viscoelasticity (2010) (2)
A variational approach to elastic wave propagation in anomalous layers (1979) (2)
The Pioneers of the Mittag-Leffler Functions in Dielectrical and Mechanical Relaxation Processes (2020) (2)
Some applications of Wright functions in fractional differential equations (2020) (2)
Wave front expansions and Pade' approximants for transient waves in linear dispersive media (1976) (2)
Applications to Stochastic Models (2020) (2)
Transient Waves in Linear Viscoelastic Media (2002) (2)
Fractional viscoelasticity (2019) (2)
Beyond the Poisson renewal process (2007) (2)
Non-Boltzmann Equilibrium Probability Densities for Non-Linear L\'{e}vy Oscillator (2000) (2)
Lévy Stable Distributions in the Theory of Probability (2007) (2)
Transient waves in finite viscoelastic rods (1980) (2)
SUBORDINATION IN FRACTIONAL DIFFUSION PROCESSES VIA CONTINUOUS TIME RANDOM WALK (2009) (2)
On the seismic pulse in a standard linear solid (1972) (2)
Reflection in liquid filled tube systems: Modelling the effects of mismatched tube segments (1987) (2)
Applications to Deterministic Models (2020) (2)
Energy propagation for dispersive waves in dissipative media (1993) (1)
The tempered space-fractional Cattaneo equation (2022) (1)
Survival probability of LIFFE bond futures via the Mittag-Leffler function (2002) (1)
International Centre for Mechanical Sciences Palazzo del Torso, Piazza Garibaldi, Udine, Italy FRACTIONAL CALCULUS : Integral and Differential Equations of Fractional Order (2008) (1)
On the scalar-wave propagation in a random elastic layer (1980) (1)
Fractional Calculus , Probability and Non-local Operators : Applications and Recent Developments November 6 th-8 th 2013 (2013) (1)
Mittag-Leffler Functions with Three Parameters (2020) (1)
Historical Overview of the Mittag-Leffler Functions (2020) (1)
Feller Fractional Diiusion and L Evy Stable Motions (1999) (1)
The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results (2021) (1)
Waves in Linear Viscoelastic Media: Dispersion and Dissipation (2010) (1)
Essentials of Fra tional Cal ulusRudolf (2000) (1)
The Role of Salvatore Pincherle in the Development of Fractional Calculus (2012) (1)
Acoustic Interactions with Submerged Elastic Structures: Part III: Acoustic Propagation and Scattering, Wavelets and Time Frequency Analysis (2001) (1)
On love’s approximation for fluid- filled elastic tubes (1980) (0)
Applications of the Method of Steepest Descents in Wave-Propagation Problems (2020) (0)
Modeling constant‐Q wave propagation with fractional derivatives (2000) (0)
Erratum: On modifications of the exponential integral with the Mittag-Leffler function (2020) (0)
An Introduction via Laplace Transform and Fractional Calculus (2012) (0)
Random Walk Models for Space-fractional Diiusion Processes Random Walk Models for Space-fractional Diiusion Processes (2007) (0)
D ec 2 00 0 NON-BOLTZMANN EQUILIBRIUM PROBABILITY DENSITIES FOR NON-LINEAR LÉVY OSCILLATOR (2008) (0)
SURVEY PAPER THE MELLIN INTEGRAL TRANSFORM IN FRACTIONAL CALCULUS (2013) (0)
Fractional calculus and special functions (2018) (0)
THE EULERIAN FUNCTIONS (2010) (0)
2 The Mittag-Leffler function in fractional relaxation processes (2020) (0)
processesfunctions and self-similar stochastic Two-particle anomalous diffusion: probability (2013) (0)
Part I: Centrovelocity for linear systems (1989) (0)
Fractional diffusion and parametric subordination (2019) (0)
Multi-index and Multi-variable Mittag-Leffler Functions (2020) (0)
Fractional calculus’s adventures in Wonderland (Round table held at ICFDA 2018) (2018) (0)
Centrovelocity for linear systems (2002) (0)
IUTAM Invited Symposium Paper Abstracts (1993) (0)
ENERGY P ROPAGATION F OR D ISPERSIVE W AVES IN DISSIPATIVE M EDIA (1993) (0)
A note on a modified fractional Maxwell model (2022) (0)
The Classical Wright Function (2020) (0)
Truncated generalized coherent states (2022) (0)
Diffusion and Wave–Propagation via Fractional Calculus (2010) (0)
Fractional relaxation with time-varying coefficient (2014) (0)
Dynamics of an impurity in a 1D periodic Burgers flow (1994) (0)
FRACTIONAL CALCULUS AND SPECIAL FUNCTIONS 1 FRACTIONAL CALCULUS AND SPECIAL FUNCTIONS (2008) (0)
FRACTIONAL RELAXATION WITH (2014) (0)
On Scott-Blair model with time-varying viscosity in linear viscoelasticity (2018) (0)
On the propagation of transient waves in a viscoelastic Bessel medium (2017) (0)
Probability Distributions and Continuous Time Random Walk 1 (2007) (0)
Kramers-Kronig relations and the analogy between electromagnetic and mechanical waves (2022) (0)
In Memoriam: Radu Balescu (2008) (0)
An approximation method to relate the linear viscoelastic functions (1982) (0)
A dynamic viscoelastic analogy for fluid-filled elastic tubes (2016) (0)
On infinite series concerning zeros of Bessel functions of the first kind (2016) (0)
in Wave Propagation Problems (2011) (0)
Publishing House "Academic Publications": Founding Publisher Prof. Drumi Bainov Editorial Board (2015) (0)
ALLONS-NOUS ? ( Contributions to Round Table Discussion held at ICFDA 2016 ) (2016) (0)
A class of linear viscoelastic models based on Bessel functions (2016) (0)
Advanced Mathematical Methods: Theory and Applications (2020) (0)
Waves in Linear Viscoelastic Media: Asymptotic Representations (2010) (0)
Random Walk Models for Time-Fractional Diffusion (2002) (0)

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What Schools Are Affiliated With Francesco Mainardi?

Francesco Mainardi is affiliated with the following schools:

Francesco Mainardi's Academic­Influence.com Rankings