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


Johan Anderson

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

Sara Moradi

Royal Military Academy

Tariq Rafiq

Lehigh University


1099-4300 (ISSN)

Vol. 20 10 760

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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