一类n维空间Riesz分数阶扩散方程的解析解  

Analytical solutions of fractional-in-space diffusion equation with Riesz fractional derivative in n dimensions

作　　者：马亮亮[1] 刘冬兵[1] 

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000

出　　处：《合肥工业大学学报（自然科学版）》2014年第4期506-509,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(60673192);四川省科技厅资助项目(2013JY0125);攀枝花学院院级培育资助项目(2012PY08);攀枝花学院校级科研资助项目(2013YB05);攀枝花学院校级科研创新资助项目(Y2013-04)

摘　　要：文章讨论了n维空间Riesz分数阶扩散方程的解,用特征函数幂级数形式定义了n维分数阶拉普拉斯算子,并给出了分数阶拉普拉斯算子与Riesz分数阶导数之间的关系,最后用谱表示法导出了n维空间Riesz分数阶扩散方程在齐次和非齐次情况下,在有界区域上满足一定初边值条件的基本解。The fundamental solutions of fractional-in-space diffusion equation with Riesz fractional de-rivative in n dimensions are considered .T he existing definitions of the fractional Laplacian in n dimen-sions are investigated by using eigenfunction expansion ,and the relations between fractional Laplacian and Riesz fractional derivative are given .Finally ,the fundamental solutions of homogeneous and non-homogeneous Riesz fractional derivative with an initial and boundary condition on a finite domain are derived by using spectral representation .

关 键 词：Riesz分数阶导数 空间分数阶扩散方程 Riemann-Liouville分数阶导数 解析解 

分 类 号：O241.82[理学—计算数学]