Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations (FPDEs) corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n -truncated representation is substituted into the original system and it is assumed the ( n − 1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The...

中文翻译：

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具有导数的浅水波分数阶微分方程耦合系统的吸引人分析技术。

非线性物理和抽象系统的数学模拟对于预测分数偏微分方程（FPDE）的求解行为（与科学和工程中的不同应用相对应）非常重要。在本文中，采用了一种有吸引力的可靠分析技术，即适形的残余幂级数，可为流体力学和流体流动中产生的一类非线性耦合FPDE构造近似序列解，这些解通常被设计用来证明弱非线性和非线性的行为。长波并描述了浅水波的相互作用。在所提出的技术中，将n截断的表示形式代入原始系统，并假定残差的（n-1）适形导数为零。这使我们能够估计出截断系数，并以快速收敛的形式在多个分数幂级数中相继添加从项。那个...