Computational Fractional Dynamical Systems
by Rajarama M. Jena, Subrat K. Jena, Snehashish Chakraverty
14Homotopy Analysis Transform Method
14.1 Introduction
A Chinese mathematician, Liao, proposed the homotopy analysis method (HAM) (Liao 2003, 2004) by using the basic definition of differential geometry and topology. Homotopy analysis transform method (HATM) is a combination of HAM and the different transform methods. This method monitors and manipulates the series solution, which converges easily to the exact solution. As a result, several authors have recently studied different phenomena using HATM (Mohamed et al. 2014; Saad and Al‐Shomrani 2016; Ziane and Cherif 2017; Maitama and Zhao 2020; Saratha et al. 2020). The HAM takes a longer time for computing and needs large computer memory. There has been a need to combine this approach with other transformation techniques to reduce the computing time and overcome other limitations. This method provides powerful features, including a nonlocal effect, a simple solution mechanism, a broad convergence region free from assumptions, discretization, and perturbation. The HATM solution involves auxiliary parameters, ℏ, which helps us to adjust and control the convergence of the series solution.