The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

Abstract

Purpose

This study aims that very lately, Mohand transform is introduced to solve the ordinary and partial differential equations (PDEs). In this paper, the authors modify this transformation and associate it with a further analytical method called homotopy perturbation method (HPM) for the fractional view of Newell–Whitehead–Segel equation (NWSE). As Mohand transform is restricted to linear obstacles only, as a consequence, HPM is used to crack the nonlinear terms arising in the illustrated problems. The fractional derivatives are taken into the Caputo sense.

Design/methodology/approach

The specific objective of this study is to examine the problem which performs an efficient role in the form of stripe orders of two dimensional systems. The authors achieve the multiple behaviors and properties of fractional NWSE with different positive integers.

Findings

The main finding of this paper is to analyze the fractional view of NWSE. The obtain results perform very good in agreement with exact solution. The authors show that this strategy is absolutely very easy and smooth and have no assumption for the constriction of this approach.

Research limitations/implications

This paper invokes these two main inspirations: first, Mohand transform is associated with HPM, secondly, fractional view of NWSE with different positive integers.

Practical implications

In this paper, the graph of approximate solution has the excellent promise with the graphs of exact solutions.

Social implications

This paper presents valuable technique for handling the fractional PDEs without involving any restrictions or hypothesis.

Originality/value

The authors discuss the fractional view of NWSE by a Mohand transform. The work of the present paper is original and advanced. Significantly, to the best of the authors’ knowledge, no such work has yet been published in the literature.

Citation

Nadeem, M., He, J.-H. and Islam, A. (2021), "The homotopy perturbation method for fractional differential equations: part 1 Mohand transform", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 11, pp. 3490-3504. https://doi.org/10.1108/HFF-11-2020-0703