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

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 .