Large Lattice Fractional Fokker-Planck Equation

TL;DR

This paper introduces a three-dimensional lattice-based fractional Fokker-Planck equation modeling anomalous diffusion, bridging microstructural lattice dynamics with continuum space-fractional diffusion equations.

Contribution

It provides a novel lattice derivation of space-fractional Fokker-Planck equations, offering a microstructural basis for non-local anomalous diffusion.

Findings

Derivation of lattice fractional Fokker-Planck equations

Continuum limit yields space-fractional diffusion equations

Links microstructure to non-local diffusion processes

Abstract

Equation of long-range particle drift and diffusion on three-dimensional physical lattice is suggested. This equation can be considered as a lattice analogof space-fractional Fokker-Planck equation for continuum. The lattice approach gives a possible microstructural basis for anomalous diffusion in media that are characterized by the non-locality of power-law type. In continuum limit the suggested three-dimensional lattice Fokker-Planck equations give fractional Fokker-Planck equations for continuous media with power-law non-locality that is described by derivatives of non-integer orders. The consistent derivation of the fractional Fokker-Planck equation is proposed as a new basis to describe space-fractional diffusion processes.