  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 related random walk models. The fundamental solution
(for the {Cauchy} problem) of the fractional diffusion equations can be
interpreted as a probability density evolving in time of a peculiar
self-similar stochastic process that we view as a generalized diffusion
process. By adopting appropriate finite-difference schemes of solution, we
generate models of random walk discrete in space and time suitable for
simulating random variables whose spatial probability density evolves in time
according to a given fractional diffusion equation.
