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.

中文翻译：

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分数阶微分方程的同伦微扰法：第1部分莫汉德变换

目的

本研究旨在最近引入莫汉德变换来求解常微分方程和偏微分方程 (PDE)。在本文中，作者修改了这种变换，并将其与一种称为同伦微扰法 (HPM) 的进一步分析方法相关联，用于 Newell-Whitehead-Segel 方程 (NWSE) 的分数视图。由于莫汉德变换仅限于线性障碍物，因此，HPM 用于破解所示问题中出现的非线性项。分数导数被考虑到卡普托意义上。

设计/方法/方法

本研究的具体目标是研究以二维系统的条形阶数形式发挥有效作用的问题。作者实现了具有不同正整数的分数 NWSE 的多种行为和属性。

发现

本文的主要发现是分析 NWSE 的分数视图。得到的结果与精确解非常吻合。作者表明，这种策略绝对非常简单和流畅，并且对这种方法的限制没有任何假设。

研究限制/影响

本文引用了这两个主要灵感：首先，莫汉德变换与 HPM 相关联，其次，具有不同正整数的 NWSE 的分数视图。

实际影响

在本文中，近似解图与精确解图具有很好的前景。

社会影响

本文介绍了在不涉及任何限制或假设的情况下处理分数 PDE 的有价值的技术。

原创性/价值

作者通过莫汉德变换讨论了 NWSE 的分数视图。本文的工作具有原创性和先进性。值得注意的是，据作者所知，尚未在文献中发表此类作品。