Revisiting the derivation of the fractional diffusion equation
arXiv:cond-mat/0210166 · doi:10.1142/9789812778109_0029
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.
Paper presented at the International Workshop on Scaling and Disordered Systems, Paris, France, 13-14 April 2000