Large lattice fractional FokkerPlanck equation
Abstract
An equation of longrange particle drift and diffusion on a 3D physical lattice is suggested. This equation can be considered as a lattice analog of the spacefractional FokkerPlanck equation for continuum. The lattice approach gives a possible microstructural basis for anomalous diffusion in media that are characterized by the nonlocality of power law type. In continuum limit the suggested 3D lattice FokkerPlanck equations give fractional FokkerPlanck equations for continuous media with power law nonlocality that is described by derivatives of noninteger orders. The consistent derivation of the fractional FokkerPlanck equation is proposed as a new basis to describe spacefractional diffusion processes.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 September 2014
 DOI:
 10.1088/17425468/2014/09/P09036
 arXiv:
 arXiv:1503.03636
 Bibcode:
 2014JSMTE..09..036T
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 27 pages, LaTeX, 8 figures