Computational Fractional Dynamical Systems

18(G′/G²)‐Expansion Method

18.1 Introduction

Exact solutions to nonlinear fractional differential equations (FDEs) play a vital role in nonlinear science. Several mathematical approaches (Diethelm et al. 2002; Erturk and Momani 2008; Behroozifar and Ahmadpour 2017) have been developed for solving FDEs. However, finding exact solutions to nonlinear FDEs remained challenging until Li and He (Li and He 2010) proposed a fractional complex transform to convert FDEs to ordinary differential equations (ODEs), allowing all analytical methods for solving ODEs to be used to partial differential equations (PDEs). Among these methods, the new analytical method, namely (G′/G²)‐expansion method (Arshed and Sadia 2018; Mohyud‐Din and Bibi 2018; Ali et al. 2019; Hassaballa 2020), has been utilized to obtain the solutions of time and space FDEs. The (G′/G²)‐method is a comparatively new technique for finding the traveling wave solutions to nonlinear single and coupled equations that arise in physics, fluid mechanics, wave propagation, population dynamics, and other fields. This method is more efficient and reliable as compared to the (G′/G)‐expansion method. This approach yields hyperbolic, trigonometric, and rational functions as solutions. These solutions are well suited to the investigation of nonlinear physical processes. Similar to the (G′/G)‐expansion method, it also allows us to find the exact solution of FDEs without initial or boundary conditions. Again, the exact solutions can be ...