  In this paper we present a study of anomalous diffusion using a Fokker-Planck
description with fractional velocity derivatives. The distribution functions
are found using numerical means for varying degree of fractionality observing
the transition from a Gaussian distribution to a L\'evy distribution. The
statistical properties of the distribution functions are assessed by a
generalized expectation measure and entropy in terms of Tsallis statistical
mechanics. We find that the ratio of the generalized entropy and expectation is
increasing with decreasing fractionality towards the well known so-called
sub-diffusive domain, indicating a self-organising behavior.
