分离变量法解三维的分数阶扩散-波动方程的初边值问题  

Separation of variables method for fractional diffusion-wave equation with initial-boundary value problem in three dimensions

作　　者：王学彬[1] 刘发旺[2] 

机构地区：[1]武夷学院经济与数学系,武夷山福建354300 [2]厦门大学数学科学学院

出　　处：《福州大学学报（自然科学版）》2007年第4期520-525,共6页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10271098)

摘　　要：考虑在有限区间上三维的时间分数阶扩散-波动方程的初边值问题.当时间分数阶导数的阶α从0变到2时,解的性态变化从慢的扩散到传统的扩散,再到混合扩散-波动.利用分离变量法,分别导出三维的非齐次时间分数阶扩散方程和非齐次时间分数阶扩散-波动方程的初边值问题的基本解.A time fractional diffusion - wave equation with initial - boundary problem in a finite domain in three dimensions （FDWEIBP_ 3D） is considered. As the order of time derivative changes from 0 to 2, the solution behaviour changes from slow diffusion to classical diffusion to mixed diffusion - wave behaviour. Using separation of variables method, the fundamental solutions of a non - homogeneous time fractional diffusion equation and a non - homogeneous time fractional diffusion - wave equation with initial -boundary problem in three-dimensions are derived, respectively.

关 键 词：分数阶扩散-波动方程 初边值问题 分离变量法 CAPUTO导数 

分 类 号：O241.82[理学—计算数学]