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

Authors
Barkai, E Metzler, R Klafter, J
Citation
E. Barkai et al., From continuous time random walks to the fractional Fokker-Planck equation, PHYS REV E, 61(1), 2000, pp. 132-138
Citations number
39
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
61
Issue
1
Year of publication
2000
Pages
132 - 138
Database
ISI
SICI code
1063-651X(200001)61:1<132:FCTRWT>2.0.ZU;2-6
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 describ es anomalous diffusion in an external force field and close to thermal equi librium. We discuss the domain of validity of the fractional kinetic equati on. For the force free case we compare between the CTRW solution and that o f the FFPE.