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

Book chapter, 2018

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 L´evy 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 L´evy 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.