From continuous time random walks to the fractional Fokker-Planck equation

E. Barkai, R. Metzler, J. Klafter

Research output: Contribution to journalArticlepeer-review

195 Scopus citations

Abstract

We generalize the continuous time random walk (CTRW) to include the effect of space dependent jump probabilities. When the mean waiting time diverges we derive a fractional Fokker-Planck equation (FFPE). This equation describes anomalous diffusion in an external force field and close to thermal equilibrium. We discuss the domain of validity of the fractional kinetic equation. For the force free case we compare between the CTRW solution and that of the FFPE.

Original languageEnglish
Pages (from-to)132-138
Number of pages7
JournalPhysical Review E
Volume61
Issue number1
DOIs
StatePublished - 2000
Externally publishedYes

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