二维Caputo型时间分数阶热传导方程非齐次初边值问题的研究  

Study on Nonhomogeneous Initial Boundary Value Problems of Two-Dimensional Caputo Type Time Fractional Heat Conduction Equation

作　　者：侯雪 欧志英[1] 

机构地区：[1]兰州理工大学理学院,甘肃 兰州

出　　处：《建模与仿真》2022年第4期987-999,共13页Modeling and Simulation

摘　　要：本文基于Povstenko型分数阶热弹性理论推导出Caputo型时间分数阶热传导方程,应用分离变量法和Laplace变换法,求解了二维有热源项的时间分数阶热传导方程的非齐次初边值问题,并给出详细的求解过程。最后通过具体的算例,分析了分数阶阶数 在不同的初边值条件下对于热传导过程的影响。In this paper, Caputo type time fractional heat conduction equation is derived based on Povstenko type fractional thermoelasticity theory. The nonhomogeneous initial boundary value problem of two-dimensional time fractional heat conduction equation with heat source term is solved by using variable separation method and Laplace transform method, and the detailed solution process is given. Finally, through a specific example, the influence of fractional order  on heat conduction process under different initial and boundary value conditions is analyzed.

关 键 词：Caputo型分数阶热传导方程 分离变量法 非齐次边界条件 

分 类 号：O17[理学—数学]