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Publications Influence

Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models

- F. Mainardi
- Mathematics
- 18 May 2010

Essentials of Fractional Calculus Essentials of Linear Viscoelasticity Fractional Viscoelastic Media Waves in Linear Viscoelastic Media: Dispersion and Dissipation Waves in Linear Viscoelastic Media:… Expand

969 57- PDF

Fractional Calculus: Integral and Differential Equations of Fractional Order

- R. Gorenflo, F. Mainardi
- Mathematics, Physics
- 25 May 2008

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the… Expand

1,158 51- PDF

Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics

- F. Mainardi
- Physics, Mathematics
- 4 January 2012

We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in… Expand

1,008 40- PDF

Mittag-Leffler Functions, Related Topics and Applications

- R. Gorenflo, A. A. Kilbas, F. Mainardi, S. Rogosin
- Mathematics
- 20 October 2014

As a result of researchers and scientists increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions… Expand

446 29- PDF

The fundamental solution of the space-time fractional diffusion equation

- F. Mainardi, Y. Luchko, G. Pagnini
- Mathematics, Physics
- 18 February 2007

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a… Expand

651 23- PDF

Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena

- F. Mainardi
- Mathematics
- 1 September 1996

Abstract The processes involving the basic phenomena of relaxation, diffusion, oscillations and wave propagation are of great relevance in physics; from a mathematical point of view they are known to… Expand

764 23

The fundamental solutions for the fractional diffusion-wave equation

- F. Mainardi
- Mathematics
- 1 November 1996

Abstract The time fractional diffusion-wave equation is obtained from the classical diffusion or wave equation by replacing the first- or second-order time derivative by a fractional derivative of… Expand

513 21

On Mittag-Leffler-type functions in fractional evolution processes

- F. Mainardi, R. Gorenflo
- Mathematics, Physics
- 1 June 2000

Abstract We review a variety of fractional evolution processes (so defined being governed by equations of fractional order), whose solutions turn out to be related to Mittag-Leffler-type functions.… Expand

469 21

Creep, relaxation and viscosity properties for basic fractional models in rheology

- F. Mainardi, G. Spada
- Mathematics, Physics
- 4 April 2011

Abstract.The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze… Expand

280 20- PDF

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