New exact solutions for time-fractional Kaup-Kupershmidt equation using improved (G′/G)-expansion and extended (G′/G)-expansion methods

Abstract

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.

Keywords

• Improved (G′/G)-expansion method
• Extended (G′/G)-expansion method
• Time-fractional Kaup-Kupershmidt equation