# Fractional Fokker-Planck Equation for Ultraslow Kinetics

Source: [Fractional Fokker-Planck Equation for Ultraslow Kinetics](<https://www.sota2.com/research/paper/68fa26052c2a3760193b5dd6>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:06:39.502Z

Authors: A. V. Chechkin, J. Klafter, I. M. Sokolov

Published: 2003-01-24T17:00:29.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0301487>)

[PDF](<https://arxiv.org/pdf/cond-mat/0301487.pdf>)