734 citations · 1.6k across the 35 of their papers we have counts for
7 papers · 1 filter
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,…
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
Francesco Mainardi, Gianni Pagnini
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-B…
Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals
Francesco Mainardi, Gianni Pagnini
The 1888 paper by Salvatore Pincherle (Professor of Mathematics at the University of Bologna) on generalized hypergeometric functions is revisited. We point out the pioneering cont…
The fundamental solution of the space-time fractional diffusion equation
Francesco Mainardi, Yuri Luchko, Gianni Pagnini
We deal with the Cauchy problem for the space-time fractional diffusion-wave equation, which is obtained from the standard diffusion equation by replacing the second-order space de…
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…
Discrete random walk models for space-time fractional diffusion
Rudolf Gorenflo, Francesco Mainardi, Daniele Moretti +2
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and relate…