In this study, we investigate a couple of nonlinear fractional differential equations namely, the sine-Gordon and Burgers equations in the sense of Riemann-Liouville fractional derivative. In order to examine exact solutions effectively applicable in relaxation and diffusion problems, crystal defects, solid-state physics, plasma physics, vibration theory, astrophysical fusion plasmas, scalar electrodynamics, etc. we introduce the new generalized -expansion method. The method is highly effective and a functional mathematical scheme to examine solitary wave solutions to diverse fractional physical models.

中文翻译：

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研究非线性时空分数正弦-Gordon和Burgers方程的新方法

在这项研究中，我们研究了几个非线性分数阶微分方程，即从Riemann-Liouville分数阶导数意义上的正弦Gordon和Burgers方程。为了研究有效解决松弛和扩散问题，晶体缺陷，固态物理学，等离子体物理学，振动理论，天体聚变等离子体，标量电动力学等的精确解，我们引入了新的广义扩展方法。该方法非常有效，并且是一种功能数学方案，可以检查各种分数物理模型的孤立波解。