Deriving fractional fokker-planck equations from a generalised master equation

R. Metzler, E. Barkai, J. Klafter

Research output: Contribution to journalArticlepeer-review

287 Scopus citations

Abstract

A generalised master equation is constructed from a non-homogeneous random walk scheme. It is shown how fractional Fokker-Planck equations for the description of anomalous diffusion in external fields, recently proposed in the literature, can be derived from this framework. Long-tailed waiting time distributions which cause slowly decaying memory effects, are demonstrated to give rise to a time-fractional Fokker-Planck equation that describes systems close to thermal equilibrium. An extension to include also Lévy flights leads to a generalised Laplacian in the corresponding fractional Fokker-Planck equation.

Original languageEnglish
Pages (from-to)431-436
Number of pages6
JournalEPL
Volume46
Issue number4
DOIs
StatePublished - 15 May 1999
Externally publishedYes

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