Anomalous Diffusion by the Fractional Fokker-Planck Equation and Lévy Stable Processes

The work presented here is a review of current developments in modelling anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives and Langevin dynamics where Levy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degree of fractionality of the stable Levy distribution as solutions to the Fokker-Planck equation and is compared to results from Langevin simulations. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics.