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Computational Fractional Dynamical Systems
book

Computational Fractional Dynamical Systems

by Rajarama M. Jena, Subrat K. Jena, Snehashish Chakraverty
November 2022
Intermediate to advanced content levelIntermediate to advanced
272 pages
8h 17m
English
Wiley
Content preview from Computational Fractional Dynamical Systems

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.

14.2 Transform Methods for the Caputo Sense Derivative

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Publisher Resources

ISBN: 9781119696957Purchase Link