Fractional derivative is nonlocal, which is more suitable to simulate physical phenomena and provides more accurate models of physical systems such as earthquake vibration and polymers. The present study suggested a new numerical approach for the fractional diffusion-wave equation (FDWE). The fractional-order derivative is in the Riemann-Liouville (R-L) sense. Discussed the theoretical analysis of stability, consistency, and convergence. The numerical examples demonstrate that the method is more workable and excellently holds the theoretical analysis, showing the scheme’s feasibility.

中文翻译：

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一维分数阶扩散波方程求解的新数值方法

分数导数是非局部的，它更适合于模拟物理现象，并提供物理系统（如地震振动和聚合物）的更精确模型。本研究为分数扩散波方程（FDWE）提出了一种新的数值方法。分数阶导数在Riemann-Liouville（RL）的意义上。讨论了稳定性，一致性和收敛性的理论分析。数值算例表明，该方法是可行的，并且很好地保留了理论分析，表明了该方案的可行性。