2 + 1维Caputo型时间分数阶膜振动方程的各种精确解
Different Kinds of Exact Solutions to 2 + 1-Dimensional Time Fractional Membrane Vibration Equation of Caputo Type
摘要: 本文利用变量分离法研究了一个2 + 1维Caputo型时间分数阶膜振动方程的精确求解问题。通过Laplace变换及其逆变换，在一定的初始条件下，借助于Bessel方程的解的相关性质，系统地对此方程的解进行了研究，获得了Caputo型时间分数阶膜振动方程的几种精确解的一般表达式。
Abstract: In this paper, the exact solution of a 2 + 1-dimensional time fractional membrane vibration equa-tion of Caputo type is studied by using the separation method of variables. Through Laplace trans-formation and its inverse transformation, under certain initial conditions, with the help of the rele-vant properties of the solution of Bessel equation, the solutions of this equation are studied sys-tematically, and the general expressions of several exact solutions of time fractional membrane vi-bration equation of Caputo type are obtained.
文章引用：李文. 2 + 1维Caputo型时间分数阶膜振动方程的各种精确解[J]. 应用数学进展, 2022, 11(7): 4537-4542. https://doi.org/10.12677/AAM.2022.117480

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