In this article, we study the numerical technique for variable‐order fractional reaction‐diffusion and subdiffusion equations that the fractional derivative is described in Caputo's sense. The discrete scheme is developed based on Lucas multiwavelet functions and also modified and pseudo‐operational matrices. Under suitable properties of these matrices, we present the computational algorithm with high accuracy for solving the proposed problems. Modified and pseudo‐operational matrices are employed to achieve the nonlinear algebraic equation corresponding to the proposed problems. In addition, the convergence of the approximate solution to the exact solution is proven by providing an upper bound of error estimate. Numerical experiments for both classes of problems are presented to confirm our theoretical analysis.

中文翻译：

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基于卢卡斯多小波函数的新颖的直接方法，用于阶变分数阶反应扩散和子扩散方程

在本文中，我们研究了分数阶微分反应扩散和子扩散方程的数值技术，其中分数导数以Caputo的意义描述。离散方案是基于Lucas多小波函数以及修改和伪运算矩阵开发的。在这些矩阵的适当性质下，我们提出了一种高精度的计算算法来解决所提出的问题。使用修正的伪运算矩阵来实现与所提出的问题相对应的非线性代数方程。另外，通过提供误差估计的上限证明了近似解与精确解的收敛性。提出了两种问题的数值实验，以证实我们的理论分析。