The study of nonlinear physical and abstract systems is greatly important in order to determine the behavior of the solutions for Fractional Partial Differential Equations (FPDEs). In this paper, we study the analytical wave solutions of the time-fractional coupled Whitham–Broer–Kaup (WBK) equations under the meaning of conformal fractional derivative. These solutions are derived using the modified extended tanh-function method. Accordingly, different new forms of the solutions are obtained. In order to understand its behavior under varying parameters, we give the visual representations of all the solutions. Finally, the graphs are discussed and a conclusion is given.

中文翻译：

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非线性适形时间分数耦合Whitham-Broer-Kaup方程的解析新孤子波解

非线性物理和抽象系统的研究对于确定分数偏微分方程 (FPDE) 解的行为非常重要。在本文中，我们研究了保形分数导数含义下的时间分数耦合Whitham-Broer-Kaup（WBK）方程的解析波解。这些解是使用改进的扩展正切函数方法推导出来的。因此，获得了不同的新形式的解决方案。为了理解它在不同参数下的行为，我们给出了所有解决方案的可视化表示。最后对图表进行了讨论并给出了结论。