From continuous time random walks to the fractional fokker-planck equation

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 equi...

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Bibliographic Details
Published in:Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000-01, Vol.61 (1), p.132-138
Main Authors: Barkai, E, Metzler, R, Klafter, J
Format: Article
Language:English
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Summary: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.
ISSN:1063-651X
1095-3787
DOI:10.1103/physreve.61.132