合肥工业大学学报(自然科学版)
閤肥工業大學學報(自然科學版)
합비공업대학학보(자연과학판)
JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY(NATURAL SCIENCE)
2014年
4期
506-509
,共4页
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
Riesz分數階導數%空間分數階擴散方程%Riemann-Liouville分數階導數%解析解
Riesz분수계도수%공간분수계확산방정%Riemann-Liouville분수계도수%해석해
Riesz fractional derivative%fractional-in-space diffusion equation%Riemann-Liouville frac-tional derivative%analytical solution
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。
文章討論瞭 n維空間Riesz分數階擴散方程的解,用特徵函數冪級數形式定義瞭 n維分數階拉普拉斯算子,併給齣瞭分數階拉普拉斯算子與 Riesz分數階導數之間的關繫,最後用譜錶示法導齣瞭 n維空間Riesz分數階擴散方程在齊次和非齊次情況下,在有界區域上滿足一定初邊值條件的基本解。
문장토론료 n유공간Riesz분수계확산방정적해,용특정함수멱급수형식정의료 n유분수계랍보랍사산자,병급출료분수계랍보랍사산자여 Riesz분수계도수지간적관계,최후용보표시법도출료 n유공간Riesz분수계확산방정재제차화비제차정황하,재유계구역상만족일정초변치조건적기본해。
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 .