Extension of natural transform method with Daftardar-Jafari polynomials for fractional order differential equations

This article aims to introduce a new method, called the Natural Transform Iterative Method (NTIM) for the solution of fractional order differential equations. The natural transform iterative method is a modification to the natural transform decomposition method (NTDM) in which Daftardar-Jafari polynomials is replaced by the Adomian polynomials. The proposed method is the combination of natural transformation and the New Iterative Method (NIM). Secondly, the comparative analysis of both methods is made for fractional-order differential equations. The fractional-order Damped Burger and fractional order Sharma-Tasso-Olver equations are taken as test examples. The beauty of the methods is that there is no need for any small or large parameter assumptions in the problem. The results obtained by proposed methods are compared by different graphs and tables, which reveals the efficiency and consistency of the NTIM over the existing NTDM. The efficiency of the proposed methods can be further improved by taking higher iterations. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

This article introduces a new method known as the Natural Transform Iterative Method (NTIM) for solving fractional order differential equations, and compares its efficiency and consistency with the existing Natural Transform Decomposition Method (NTDM) using test examples. The results suggest that NTIM is more efficient and consistent than NTDM.