Computational Fractional Dynamical Systems

16q‐Homotopy Analysis Transform Method

16.1 Introduction

A Chinese mathematician, Liao, proposed the homotopy analysis method (HAM) (Liao 2003, 2004) by employing the fundamental concept of differential geometry and topology. HAM has recently been used effectively to obtain solutions to problems in various fields of science and technology. In accordance with this, the q‐homotopy analysis transform method (q‐HATM) was developed, which is a combination of q‐HAM and the different transform methods. This method monitors and manipulates the series solution, which converges to the exact solution. As a result, several authors have recently studied different phenomena using q‐HATM (Srivastava et al. 2017; Jena and Chakraverty 2019; Veeresha et al. 2019; Jena et al. 2020; Veeresha and Prakasha 2020). The HAM takes longer for computing and large computer memory. There has been a need to integrate this technique with transformation techniques to address these limitations. The present method has many strong properties, including a nonlocal effect, a simple solution procedure, a broad convergence region free from assumptions, discretization, and perturbation. It is worth mentioning that the transform methods with semi‐analytical techniques require less CPU time to evaluate the solutions for nonlinear fractional complex models. Again, the q‐HATM solution involves two auxiliary parameters, n and ℏ, which help us to adjust and control the convergence of the solution.

16.2 Transform Methods ...