Applications of integral transforms in fractional diffusion processes
Probability
2007-10-02 v1 Complex Variables
Abstract
The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then, by using the Mellin transform, a general representation of the Green function in terms of Mellin-Barnes integrals in the complex plane is derived. This allows us to obtain a suitable computational form of the Green function in the space-time domain and to analyse its probability interpretation.
Cite
@article{arxiv.0710.0145,
title = {Applications of integral transforms in fractional diffusion processes},
author = {Francesco Mainardi},
journal= {arXiv preprint arXiv:0710.0145},
year = {2007}
}
Comments
11 Pages. Paper with added notes based on an invited lecture: 3rd International ISAAC Congress, Free University of Berlin, 20-25 August 2001 (Sub-session 1.3: Integral Transforms and Applications)