Three nonlinear fractional models, videlicet, the space-time fractional Boussinesq equation, -dimensional breaking soliton equations, and SRLW equation, are the important mathematical approaches to elucidate the gravitational water wave mechanics, the fractional quantum mechanics, the theoretical Huygens’ principle, the movement of turbulent flows, the ion osculate waves in plasma physics, the wave of leading fluid flow, etc. This paper is devoted to studying the dynamics of the traveling wave with fractional conformable nonlinear evaluation equations (NLEEs) arising in nonlinear wave mechanics. By utilizing the oncoming -expansion technique, a series of novel exact solutions in terms of rational, periodic, and hyperbolic functions for the fractional cases are derived. These types of long-wave propagation phenomena played a dynamic role to interpret the water waves as well as mathematical physics. Here, the form of the accomplished solutions containing the hyperbolic, rational, and trigonometric functions is obtained. It is demonstrated that our proposed method is further efficient, general, succinct, powerful, and straightforward and can be asserted to install the new exact solutions of different kinds of fractional equations in engineering and nonlinear dynamics.

中文翻译：

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三种非线性分数模型的纯行波解

三种非线性分数模型videlicet，时空分数 Boussinesq方程， -维分解孤子方程和SRLW方程是阐明引力水波力学，分数量子力学，理论惠更斯原理，湍流运动，等离子物理学中离子振荡波，波的重要数学方法本文主要研究非线性波动力学中分数分数适形非线性评估方程（NLEE）对行波动力学的影响。利用即将来临的-扩展技术，导出了针对分数情况的有理，周期和双曲函数的一系列新颖的精确解。这些类型的长波传播现象对解释水波以及数学物理学起了动态作用。在这里，获得了包含双曲，有理和三角函数的已完成解决方案的形式。结果表明，我们提出的方法是进一步有效，通用，简洁，强大且简单的方法，可以断言在工程和非线性动力学中安装各种分数方程的新精确解。