高维非齐次时间分数阶扩散-波动方程的解析解问题

Analytical Solutions of Non-Homogeneous Time Fractional Diffusion-Wave Equation in Higher Dimensions

分数阶微积分是专门研究任意阶积分和微分的数学性质及其应用的领域,是传统的整数阶微积分的推广,分数阶微分方程是含有非整数阶导数的方程.时间分数阶扩散-波动方程可以用来模拟由传统的扩散-波动方程演变而来的反常扩散方程.考虑在有限区间上高维非齐次时间分数阶扩散-波动方程的初边值问题.利用分离变量法,导出了高维非齐次时间分数阶扩散-波动方程初边值问题的基本解.

Fractional calculus is a branch of studying the property of any order integral or derivative. Fractional order differential equation is the equation containing the non-integer derivative, raising from the standard differential derivatives with fractional-order derivatives. Time equations by replacing the integer-order fractional diffusion-wave equation, which is different from traditional diffusion-wave equation, can be utilized to simulate time-related anomalous diffusion. In this paper, a non-homogeneous time fractional diffusion-wave equation with initial-boundary value problem in a finite domain in higher dimensions is considered. Us- ing the separation of variables method, the fundamental solutions of a non-homogeneous time fractional diffusion-wave equation with initial-boundary value problem in higher dimensions is derived.