Computational Fractional Dynamical Systems

6Homotopy Perturbation Transform Method

6.1 Introduction

In Chapter 5, we have already discussed the homotopy perturbation method (HPM), which is a semi‐analytical approach for solving linear and nonlinear ordinary/partial/fractional differential equations. In this chapter, we will discuss about the hybrid methods, which are the coupling of HPM with various transform methods, viz. Laplace transform (LT), Sumudu transform (ST), Elzaki transform (ET), and Aboodh transform (AT). As said earlier, HPM with the combination of these transform methods is called as homotopy perturbation transform method (HPTM) (Singh and Kumar 2011, 2012; Elzaki and Biazar 2013; Mahdy et al. 2015; Mohand and Mahgoub 2016; Sedeeg 2016; Olubanwo et al. 2019). Nowadays, these methods, namely homotopy perturbation Laplace transform method (HPLTM), homotopy perturbation Sumudu transform method (HPSTM), homotopy perturbation Elzaki transform method (HPETM), and homotopy perturbation Aboodh transform method (HPATM), are getting popular recently. Although these four transform methods are effective methods for solving fractional differential equations, but these methods sometimes fail to address nonlinear terms arising from the fractional differential equations. These difficulties may be overcome by coupling these transforms with that of HPM. In the subsequent sections, the theories behind the four transform methods with respect to fractional order are given. Then the systematic study of the earlier‐mentioned ...