求解分形介质中分数阶扩散模型的相似方法(英文)  

Similarity Method to Solve Fractional Diffusion Model in Fractal Media

作　　者：段俊生[1] 郭爱平[2] 云文在[2] 

机构地区：[1]上海应用技术学院理学院,上海201418 [2]包头师范学院数学科学学院,内蒙古包头014030

出　　处：《生物数学学报》2010年第2期218-224,共7页Journal of Biomathematics

基　　金：Supported by the Research Foundation of Shanghai Institute of Technology(YJ 2009-12)

摘　　要：分形介质中输运现象的分数阶扩散方程是一个积分-偏微分方程,含有由分形Hausdorff维数d_f和反常扩散指数d_w确定的参数.对于这类方程的求解问题,给出了尺度变换群的不变子并且导出了关于尺度不变解的积分-常微分方程.最后利用Mellin变换和Fox函数得到尺度不变解.Fractional diffusion equation for transport phenomena in fractal media is an integro-partial differential equation with the parameters determined by the fractal Hausdorff dimension dI and the anomalous diffusion exponent dw. For the solving problem of this kind of equation the invariants of the group of scaling transformations are given and then used for deriving the integro-ordinary differential equation for the scale-invariant solution. With the help of Mellin transform and Fox functions the exact scale-invariant solution is obtained eventually.

关 键 词：分数阶微积分 反常扩散 不变子 Fox函数 

分 类 号：O175.6[理学—数学] O791[理学—基础数学]