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From Power Laws to Fractional Diffusion: the Direct Way
Rudolf Gorenflo, Entsar A. A. Abdel-Rehim
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails c…
Some aspects of fractional diffusion equations of single and distributed order
Francesco Mainardi, Gianni Pagnini, Rudolf Gorenflo
The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $β\in (0,…
Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk
Rudolf Gorenflo, Francesco Mainardi
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations…
Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects
Rudolf Gorenflo, Francesco Mainardi
We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional…
Probability distributions generated by fractional diffusion equations
Francesco Mainardi, Paolo Paradisi, Rudolf Gorenflo
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a deriv…
Mellin transform and subordination laws in fractional diffusion processes
Francesco Mainardi, Gianni Pagnini, Rudolf Gorenflo
The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted…