Anomalous diffusion by the fractional Fokker-Planck equation and Levy 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.
Fractional Fokker-Plank Equation.