用于超慢动力学的分数阶福克-普兰克方程
统计力学
2009-11-10 v1 无序系统与神经网络
摘要
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.
引用
@article{arxiv.cond-mat/0301487,
title = {Fractional Fokker-Planck Equation for Ultraslow Kinetics},
author = {A. V. Chechkin and J. Klafter and I. M. Sokolov},
journal= {arXiv preprint arXiv:cond-mat/0301487},
year = {2009}
}