The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP)
equation are studied estimating the generalized diffusion coefficients. The~aim
is to model anomalous diffusion using an FFP description with fractional
velocity derivatives and Langevin dynamics where L\'{e}vy 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 degrees of fractionality of the stable L\'{e}vy distribution
as solutions to the FFP equation. The~statistical properties of the
distribution functions are assessed by a generalized normalized expectation
measure and entropy and modified transport coefficient. The~transport
coefficient significantly increases with decreasing fractality which is
corroborated by analysis of experimental data.Comment: 20 pages 7 figure
