Solution of a modified fractional diffusion equation
Solution of a modified fractional diffusion equation
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DOI：
10.1016/j.physa.2005.12.012
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发表时间：
2006-07
影响因子：
3.3
通讯作者：
T. Langlands
中科院分区：
文献类型：
--
作者：
T. Langlands
最近，提出了一个改进的分数扩散方程[1]。Sokolov， J. Klafter，从扩散到反常扩散：爱因斯坦布朗运动后的一个世纪，混沌15 (2005)026103；A.V. checchkin， R. Gorenflo， I.M. Sokolov， V.Yu。Gonchar，分布阶时间分数扩散方程。Calc .。肛门。6 (3)(2003)259279；李建军，李建军，李建军，分布阶分数动力学，学报。理论物理。波尔。B 35(2004) 1323。通过包含作用于扩散项的第二个分数阶时间导数来描述随着时间的推移而变得不那么反常的过程。在这封信中，我们给出了修正方程在无限定义域上的解。与传统分数扩散方程的解相比，修正方程的解需要无穷级数的Fox函数而不是单个Fox函数。
Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.