This paper deals with the optical solitons of fractional coupled Boussinesq, Burgers-type and mKdV equations by the hypothesis of traveling wave and G′ G2-expansion scheme. These equations are important in different fields such as propagation of long water waves, fluid dynamics, and shallow water wave propagation. In comparison to other analytical procedures, the analytical methodology G′ G2 is an incredibly beneficial approach. This technique can also be used with other nonlinear fractional models. The suggested method generates three distinct solutions such as trigonometric, hyperbolic, and rational. Moreover, graphical representation has been used to portray the physical significance of the constructed solutions. Finally, a comprehensive study is made by using a definition of Beta fractional derivative and obtained solutions are represented graphically to understand considered models.

中文翻译：

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数学物理中出现的三个重要耦合模型的多种分数孤子解

本文通过行波假设和 G' G2- 扩展方案。这些方程在长水波传播、流体动力学和浅水波传播等不同领域都很重要。与其他分析程序相比，分析方法 G' G2是一种非常有益的方法。这种技术也可以与其他非线性分数模型一起使用。建议的方法生成三种不同的解决方案，例如三角函数、双曲线和有理数。此外，图形表示已被用来描绘所构建解决方案的物理意义。最后，通过使用 Beta 分数导数的定义进行全面研究，并以图形方式表示获得的解决方案以理解所考虑的模型。