Computational Fractional Dynamical Systems

24Exp‐Function Method

24.1 Introduction

He and Wu (2006) were the first to suggest the exp‐function method, which was effectively used to find solitary and periodic solutions to nonlinear partial differential equations. Further, researchers have also utilized this strategy in their studies to deal with different other equations like stochastic modified Korteweg de Vries (mKDV) equation (Dai and Zhang 2009a), one‐dimensional fractional wave equation, and fractional reaction‐diffusion problem (Yildirim and Pinar 2010; Bekir et al. 2015), space–time fractional Fokas, and the nonlinear fractional Sharma‐Tasso‐Olver equations (Zheng 2013), fractional Fitzhugh‐Nagumo and KdV equations (Bekir et al. 2017), and so on (He and Abdou 2007; Wu and He 2007; Zhang 2007; Zhu 2008). This approach may be used to solve difference‐differential equations (Zhu 2007a, 2007b) and equations with variable coefficients (El‐wakil et al. 2007; Zhang 2008). The method can also be used to create n‐soliton solutions and rational solutions (Dai and Zhang 2009a; Dai and Zhang 2009b). It converts fractional partial differential equations into ordinary differential equations via fractional complex transform, simplifying the solution process. The exp‐function approach is simple and effective in obtaining generalized solitary and periodic solutions to nonlinear evolution equations. The key advantage of this approach over others is that it produces more general solutions with certain free parameters. Simplified ...