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

• Main Authors: Rashid Nawaz, Nasir Ali, Laiq Zada, Kottakkkaran Sooppy Nisar, M.R. Alharthi, Wasim Jamshed
• Format: Article
• Language: English
• Published: Elsevier 2021-06-01
• Series: Alexandria Engineering Journal
• Subjects: NTIM; NTDM; Damped Burger (DB) equation; Sharma-Tasso-Olver (STO) equation; Daftardar-Jafari (DJ) polynomials
• Online Access: http://www.sciencedirect.com/science/article/pii/S1110016821000557

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.