用Allen-Cahn方程的精确解实现随机分数阶的新观点

IF 1.3 Q3 ENGINEERING, MULTIDISCIPLINARY
F. Hasan, Mohamed A. Abdoon, Rania Saadeh, Mohammed Berir, Ahmad Qazza
{"title":"用Allen-Cahn方程的精确解实现随机分数阶的新观点","authors":"F. Hasan, Mohamed A. Abdoon, Rania Saadeh, Mohammed Berir, Ahmad Qazza","doi":"10.33889/ijmems.2023.8.5.052","DOIUrl":null,"url":null,"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.","PeriodicalId":44185,"journal":{"name":"International Journal of Mathematical Engineering and Management Sciences","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Perspective on the Stochastic Fractional Order Materialized by the Exact Solutions of Allen-Cahn Equation\",\"authors\":\"F. Hasan, Mohamed A. Abdoon, Rania Saadeh, Mohammed Berir, Ahmad Qazza\",\"doi\":\"10.33889/ijmems.2023.8.5.052\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":44185,\"journal\":{\"name\":\"International Journal of Mathematical Engineering and Management Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematical Engineering and Management Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33889/ijmems.2023.8.5.052\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Engineering and Management Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33889/ijmems.2023.8.5.052","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A New Perspective on the Stochastic Fractional Order Materialized by the Exact Solutions of Allen-Cahn Equation
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信