Authors
Ralf Metzler, Eli Barkai, Joseph Klafter
Publication date
1999
Journal
Europhysics Letters
Volume
46
Issue
4
Pages
431-436
Publisher
EDP Sciences
Description
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.
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Scholar articles
R Metzler, E Barkai, J Klafter - Europhysics Letters, 1999