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
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。
Abstract: 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.
文章引用：侯雪, 欧志英. 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[J]. 建模与仿真, 2022, 11(4): 987-999. https://doi.org/10.12677/MOS.2022.114091

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