Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Levy Stable~Processes
Journal article, 2018

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.

non-local theory

Tsallis entropy

Lévy noise

fractional Fokker--Plank equation

anomalous diffusion

Author

Johan Anderson

Chalmers, Space, Earth and Environment, Astronomy and Plasmaphysics, Plasma Physics and Fusion Energy

Sara Moradi

Royal Military Academy

Tariq Rafiq

Lehigh University

Entropy

1099-4300 (ISSN)

Vol. 20 10 760

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

DOI

10.3390/e20100760

More information

Latest update

11/6/2018