高维非齐次时间分数阶电报方程的基本解  

Fundamental Solutions of the Non-Homogeneous Time Fractional Telegraph Equation in High 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：《四川师范大学学报（自然科学版）》2015年第1期77-83,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671132和60673192);四川省应用基础基金(2013JY0125)资助项目

摘　　要：分数阶微分方程在许多应用科学上比整数阶微分方程更能准确地模拟自然现象.考虑了高维非齐次时间分数阶电报方程的初边值问题,使用分离变量法导出了Dirichlet边界条件下高维非齐次时间分数阶电报方程的解析解,并给出了四维非齐次时间分数阶电报方程的解析解表达式.Many phenomena can be more correctly simulate by fractional differential equations contrasting with integer differential equations in most of applied sciences. In this paper,a non-homogeneous time fractional telegraph equation with initial-boundary value problem in high dimensions is considered,the method of separating variables is effectively implemented for solving the non-homogeneous time fractional telegraph equation with Dirichlet initial-boundary value problem in high dimensions. Finally,an analytical solution to non-homogeneous time fractional telegraph equations with Dirichlet initial-boundary value problem in four dimensions is obtained.

关 键 词：电报方程 分数阶 分离变量法 CAPUTO导数 DIRICHLET边界条件 

分 类 号：O241.82[理学—计算数学]