Computational Fractional Dynamical Systems

21Sine‐Cosine Method

21.1 Introduction

Nonlinear fractional differential equations have been studied using several approaches in recent decades. These methods may require a significant size of computational work. Several strategies have been developed to find single soliton solutions of the fractional models. It may be noted that there is no single approach that can be applied to all nonlinear fractional models. The sine‐cosine method (Wazwaz 2004b, 2004c, 2005, 2017) proposed by Wazwaz (Wazwaz 2004a) is a powerful strategy that has recently been used in various researches. Using the sine‐cosine approach, Sabi’u et al. (2019) found the exact solution for the (3 + 1) conformable space–time fractional modified Korteweg–de‐Vries equations. Alquran (2012) has obtained the periodic and bell‐shaped solitons solutions to the Benjamin‐Bona‐Mahony, the Gardner equations, and the Cassama‐Holm equation. Yusufoglu and Bekir (2006) have successfully derived many new families of exact traveling wave solutions of the (2 + 1)‐dimensional Konopelchenko–Dubrovsky equations and the coupled nonlinear Klein–Gordon and Nizhnik–Novikov–Veselov equations. Bekir (2008) successfully established exact traveling wave solutions of the symmetric regularized long‐wave (SRLW) and Klein–Gordon–Zakharov (KGZ) equations with the help of this method. The sine‐cosine method has been used to solve a broad range of nonlinear problems. Various nonlinear dispersive and dissipative equations have also been successfully ...