Fokker-Planck equation with fractional coordinate derivatives

被引：10
|
作者：
Tarasov, Vasily E. [1 ,2 ]
Zaslavsky, George M. [1 ,3 ]
机构：
[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA
[2] Moscow MV Lomonosov State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119991, Russia
[3] NYU, Dept Phys, New York, NY 10003 USA
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2008年 / 387卷 / 26期
关键词：
Fractional kinetics; Fractional derivatives; Long-range interaction; Fokker-Planck equation; Kolmogorov-Feller equation;
D O I：
10.1016/j.physa.2008.08.033
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations, with averaging with respect to a fast variable, is used. The main assumption is that the correlation function of probability densities of particles to make a step has a power-law dependence. As a result, we obtain a Fokker-Planck equation with fractional coordinate derivative of order 1 < alpha < 2. (c) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：6505 / 6512
页数：8
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