In this study, the traveling wave solutions for the time-fractional shallow water wave equation system, whose physical application is defined as the dynamics of water bodies in the ocean or seas, are investigated by (G′ G , 1 G)-expansion method. The nonlinear fractional partial differential equation is transformed to the non-fractional ordinary differential equation with the use of a special wave transformation. In this special wave transformation, we consider the conformable fractional derivative operator to which the chain rule is applied. We obtain complex hyperbolic and complex trigonometric functions for the time-fractional shallow water wave equation system with the help of this technique. New traveling wave solutions are obtained for the special values given to the parameters in these complex hyperbolic and complex trigonometric functions, and the behavior of these solutions is examined with the help of 3D and 2D graphics.

中文翻译：

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时间分数浅水波动方程组行为的动态相互作用

在这项研究中，时间分数浅水波动方程系统的行波解，其物理应用被定义为海洋或海洋中水体的动力学，研究了(G' G , 1 G)- 扩展方法。非线性分数偏微分方程通过特殊的波变换转换为非分数常微分方程。在这个特殊的波变换中，我们考虑应用链式法则的一致分数导数算子。借助该技术，我们获得了时间分数浅水波动方程组的复双曲和复三角函数。对于这些复双曲函数和复三角函数中参数的特殊值，获得了新的行波解，并在 3D 和 2D 图形的帮助下检查了这些解的行为。