In this paper, we propose a numerical scheme based on the iterative method for solving the fractional diffusion‐wave equation involving the Caputo–Weyl fractional derivative of order $0<\alpha \le 2$. The convergence of the approximate solutions of the fractional diffusion‐wave equation is rigourously established. Moreover, the approximate solutions of the fractional diffusion‐wave equation have been presented graphically.

中文翻译：

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一种求解Caputo-Weyl分数阶导数的分数阶扩散波方程的迭代方法

在本文中，我们提出了一种基于迭代方法的数值方案，用于求解涉及阶Caputo-Weyl分数阶导数的分数扩散波方程 $0<\alpha \le 2$。严格建立了分数阶扩散波方程近似解的收敛性。此外，分数阶扩散波方程的近似解已以图形方式给出。