Volume 63, Number 3, August 2003
|Page(s)||326 - 332|
|Published online||01 November 2003|
Fractional Fokker-Planck equation for ultraslow kinetics
Institute for Theoretical Physics, N SC KIPT Akademicheskaya st. 1, 61108 Kharkov, Ukraine
2 School of Chemistry, Sackler Faculty of Exact Sciences Tel Aviv University - Tel Aviv 69978, Israel
3 Institut für Physik, Humboldt-Universität zu Berlin Invalidenstrasse 110, D-10115 Berlin, Germany
Accepted: 2 June 2003
Several classes of physical systems exhibit ultraslow diffusion for which the mean-squared displacement at long times grows as a power of the logarithm of time (“strong anomaly”) and share the interesting property that the probability distribution of particle's position at long times is a double-sided exponential. We show that such behaviors can be adequately described by a distributed-order fractional Fokker-Planck equations with a power law weighting function. We discuss the equations and the properties of their solutions, and connect this description with a scheme based on continuous-time random walks.
PACS: 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, 2003
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