Applications of integral transforms in fractional diffusion processes

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.

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)