| Issue |
Europhys. Lett.
Volume 63, Number 3, August 2003
|
|
|---|---|---|
| Page(s) | 326 - 332 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2003-00539-0 | |
| Published online | 01 November 2003 | |
Fractional Fokker-Planck equation for ultraslow kinetics
1
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
Corresponding authors: achechkin@kipt.kharkov.ua klafter@post.tau.ac.il igor.sokolov@physik.hu-berlin.de
Received:
29
January
2003
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.