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Fractional Fokker-Planck Equation for Ultraslow Kinetics

A. V. Chechkin·J. Klafter·I. M. Sokolov
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Abstract

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.

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BibTeXRIS

A. V. Chechkin, J. Klafter, I. M. Sokolov. 2003-01-24. Fractional Fokker-Planck Equation for Ultraslow Kinetics. https://doi.org/10.1209/epl%2Fi2003-00539-0

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