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

E Barkai; R Metzler; J Klafter

doi:10.1103/physreve.61.132

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

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):132-8. doi: 10.1103/physreve.61.132.

Authors

E Barkai¹, R Metzler, J Klafter

Affiliation

¹ Department of Chemistry and Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.

PMID: 11046248
DOI: 10.1103/physreve.61.132

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.