In this paper, we investigate the Riemann wave model (RWM) on Cantor sets by using the local fractional derivative (LFD). A novel computational approach is provided to seek the exact traveling-wave solution of the non-differential type for the local fractional Riemann wave model (LFRWM). The proposed scheme is called local fractional traveling-wave method (LFTWM). An example is given to illustrate that the LFTWM is simple and excellent. The properties of the obtained traveling-wave solutions are elaborated by some 3D graphs. The LFTWM sheds a new light on solving the local fractional wave equations (LFWE) in physics and engineering.

中文翻译：

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海洋科学中出现的分形黎曼波模型的精确行波解

在本文中，我们使用局部分数导数（LFD）研究康托集上的黎曼波模型（RWM）。提供了一种新的计算方法来寻找局部分数黎曼波模型（LFRWM）的非微分类型的精确行波解。所提出的方案称为局部分数行波法（LFTWM）。举一个例子来说明LFTWM简单而优秀。获得的行波解的性质由一些 3D 图详细说明。LFTWM 为解决物理和工程中的局部分数波动方程 (LFWE) 提供了新的思路。