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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…
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…
Renewal processes of Mittag-Leffler and Wright type
Francesco Mainardi, Rudolf Gorenflo, Alessandro Vivoli
After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and…
A fractional generalization of the Poisson processes
Francesco Mainardi, Rudolf Gorenflo, Enrico Scalas
It is our intention to provide via fractional calculus a generalization of the pure and compound Poisson processes, which are known to play a fundamental role in renewal theory, wi…