The mathematical modeling of physical systems is generally governed by evolution equations in nonlinear form. Therefore, it is critical to obtain exact analytical solutions to these equations. This paper contains the application of improved (G′/G)-expansion and extended (G′/G)-expansion methods for establishing new analytical solutions of a nonlinear evolution equation. Mainly, improved (G′/G)-expansion and extended (G′/G)-expansion methods have been applied to time-fractional Kaup-Kupershmidt equation for getting some new general forms of exact solutions. Here, algorithms provide a more convenient and systematically handling the solution process of the non-linear evolution equations.

物理系统的数学建模通常由非线性形式的演化方程控制。因此，获取这些方程式的精确解析解至关重要。本文包含改进的（G ' / G）展开和扩展的（G ' / G）展开方法在建立非线性演化方程的新解析解中的应用。主要是改进的（G ' / G）扩展和扩展的（G ' / G））展开方法已应用于时间分数阶Kaup-Kupershmidt方程，以获取精确解的一些新通用形式。在这里，算法为非线性发展方程的求解过程提供了更方便，系统的处理方法。