A New Perspective on the Stochastic Fractional Order Materialized by the Exact Solutions of Allen-Cahn Equation

F. Hasan, Mohamed A. Abdoon, Rania Saadeh, Mohammed Berir, Ahmad Qazza
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Abstract

Stochastic fractional differential equations are among the most significant and recent equations in physical mathematics. Consequently, several scholars have recently been interested in these equations to develop analytical approximations. In this study, we highlight the stochastic fractional space Allen-Cahn equation (SFACE) as a major application of this class. In addition, we utilize the simplest equation method (SEM) with a dual sense of Brownian motion to convert the presented equation into an ordinary differential equation (ODE) and apply an effective computational technique to obtain exact solutions. By carefully comparing the derived solutions with solutions from other articles, we prove the distinction of these solutions for their diversity and the discovery of new solutions for SFACE that appear in many scientific fields, such as mathematical biology, quantum mechanics, and plasma physics. The results introduced in this article were obtained by plotting several graphs and examining how noise affects exact solutions using Mathematica and MATLAB software packages.
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用Allen-Cahn方程的精确解实现随机分数阶的新观点
随机分数阶微分方程是物理数学中最重要和最新的方程之一。因此,一些学者最近对这些方程感兴趣,以开发分析近似。在这项研究中,我们强调随机分数空间Allen-Cahn方程(SFACE)是这一类的主要应用。此外,我们利用具有布朗运动对偶意义的最简单方程方法(SEM)将所提出的方程转化为常微分方程(ODE),并应用有效的计算技术获得精确解。通过仔细比较导出的解决方案与其他文章中的解决方案,我们证明了这些解决方案的多样性,并发现了SFACE的新解决方案,这些解决方案出现在许多科学领域,如数学生物学、量子力学和等离子体物理。本文中介绍的结果是通过绘制几张图并使用Mathematica和MATLAB软件包检查噪声如何影响精确解而获得的。
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来源期刊
CiteScore
3.80
自引率
6.20%
发文量
57
审稿时长
20 weeks
期刊介绍: IJMEMS is a peer reviewed international journal aiming on both the theoretical and practical aspects of mathematical, engineering and management sciences. The original, not-previously published, research manuscripts on topics such as the following (but not limited to) will be considered for publication: *Mathematical Sciences- applied mathematics and allied fields, operations research, mathematical statistics. *Engineering Sciences- computer science engineering, mechanical engineering, information technology engineering, civil engineering, aeronautical engineering, industrial engineering, systems engineering, reliability engineering, production engineering. *Management Sciences- engineering management, risk management, business models, supply chain management.
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