In this paper, the Local Fractional Laplace Decomposition Method (LFLDM) is used for solving a type of Two-Dimensional Fractional Diffusion Equation (TDFDE). In this method, first we apply the Laplace transform and its inverse to the main equation, and then the Adomian decomposition is used to obtain approximate/analytical solution. The accuracy and applicability of the LFLDM is shown through two examples. The LFLDM results are in good agreement with the exact solution of the problems.

中文翻译：

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求解分形传热中二维扩散问题的拉普拉斯分解法

本文采用局部分数阶拉普拉斯分解法（LFLDM）来求解一类二维分数阶扩散方程（TDFDE）。在该方法中，首先对主方程应用拉普拉斯变换及其逆变换，然后使用Adomian分解来获得近似/解析解。通过两个例子说明了LFLDM的准确性和适用性。 LFLDM 结果与问题的精确解非常吻合。