Revisiting the derivation of the fractional diffusion equation

Abstract

The fractional diffusion equation is derived from the master equation of continuous-time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.Comment: Paper presented at the International Workshop on Scaling and Disordered Systems, Paris, France, 13-14 April 200