Solution of Fractional Heat-Like and Fractional Wave-Like Equation by Using Modern Strategy

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-11 DOI:10.2478/ama-2023-0042

Mohamed Z. Mohamed, A. Hamza, T. Elzaki, Mohamed S. Algolam, Shiraz Elhussein

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Abstract

Abstract This paper introduces a novel form of the Adomian decomposition (ADM) method for solving fractional-order heat-like and wave-like equations with starting and boundary value problems. The derivations are provided in the sense of Caputo. In order to help understanding, the generalised formulation of the current approach is provided. Several numerical examples of fractional-order diffusion-wave equations (FDWEs) are solved using the suggested method in this context. In addition to examining the applicability of the suggested method to the solving of fractional-order heat-like and wave-like equations, a graphical depiction of the solutions to three instructive cases was constructed. Solution graphs were arrived at for integer and fractional-order problems. The derived and exact solutions to integer-order problems were found to be in excellent agreement. The subject of the present research endeavour is the convergence of fractional-order solutions. This strategy is considered to be the most successful way of addressing fractional-order initial-boundary value issues in science and engineering. This strategy is presented here.

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用现代策略求解分数阶类热方程和分数阶类波方程

摘要本文介绍了一种新的Adomian分解(ADM)方法，用于求解具有起始值和边值问题的分数阶类热方程和类波方程。推导是在卡普托的意义上提供的。为了帮助理解，提供了当前方法的一般表述。在此背景下，用该方法求解了几个分数阶扩散波方程的数值算例。除了检验该方法在求解分数阶类热方程和类波方程中的适用性外，还构造了三个具有指导意义的实例的图形描述。得到了整数和分数阶问题的解图。发现整阶问题的推导解与精确解非常吻合。目前研究的课题是分数阶解的收敛性。该策略被认为是解决科学和工程中分数阶初边值问题的最成功的方法。本文介绍了这一策略。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.