摘要
讨论二维、三维空间Riesz分数阶扩散方程的解,用特征函数幂级数形式定义二维、三维分数阶拉普拉斯算子,并给出分数阶拉普拉斯算子与Riesz分数阶导数的关系。最后用谱表示法导出二维、三维空间Riesz分数阶扩散方程在齐次和非齐次情况下的在有界区间上满足一定初边值条件的基本解。
The fundamental solutions of fractional-in-space diffusion equation are considered with Riesz fractional deriv- ative （RFDE） in two and three dimensions. The existing definitions of the fractional Laplacian （ two dimensions and three dimensions） are investigated and discussed by using eigenfunction expansion, and the relations between fractional Laplacian and Riesz fractional derivative are given. Finally, the fundamental solutions of homogeneous and non-homo- geneous RFDE with an initial and boundary condition are derived on a finite domain using a spectral representation.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2011年第8期23-30,37,共9页
Journal of Shandong University(Natural Science)
基金
Supported by the Natural Science Foundation of Fujian Province(2008J0204)
Fujian Provincial Department of Education Category the Projects(JA09242)
Wuyi University Special Research Fund for Young Teachers(xq201022)
