In this paper, a meshless generalized finite difference method (GFDM) is proposed to solve the time fractional diffusion-wave (TFDW) equations. A second-order temporal discretization scheme is developed to tackle the Caputo fractional derivative, and then spatial discretization formulas are derived by the GFDM. Theoretical accuracy and convergence of the GFDM for TFDW equations are analyzed. Numerical results verify the theoretical results and the efficiency of the method.

中文翻译：

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广义有限差分法分数阶扩散波方程的无网格分析


本文提出了一种无网格广义有限差分法（GFDM）来求解时间分数扩散波（TFDW）方程。提出了二阶时间离散化方案来解决Caputo分数阶导数，然后通过GFDM导出空间离散化公式。分析了TFDW方程的GFDM的理论精度和收敛性。数值结果验证了理论结果和方法的有效性。