复空间中求解分数阶非线性积分-微分方程的新方法

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractal and Fractional Pub Date : 2023-10-31 DOI:10.3390/fractalfract7110796
Amnah E. Shammaky, Eslam M. Youssef, Mohamed A. Abdou, Mahmoud M. ElBorai, Wagdy G. ElSayed, Mai Taha
{"title":"复空间中求解分数阶非线性积分-微分方程的新方法","authors":"Amnah E. Shammaky, Eslam M. Youssef, Mohamed A. Abdou, Mahmoud M. ElBorai, Wagdy G. ElSayed, Mai Taha","doi":"10.3390/fractalfract7110796","DOIUrl":null,"url":null,"abstract":"This work aims to explore the solution of a nonlinear fractional integro-differential equation in the complex domain through the utilization of both analytical and numerical approaches. The demonstration of the existence and uniqueness of a solution is established under certain appropriate conditions with the use of Banach fixed point theorems. To date, no research effort has been undertaken to look into the solution of this integro equation, particularly due to its fractional order specification within the complex plane. The validation of the proposed methodology was performed by utilizing a novel strategy that involves implementing the Rationalized Haar wavelet numerical method with the application of the Bernoulli polynomial technique. The primary reason for choosing the proposed technique lies in its ability to transform the solution of the given nonlinear fractional integro-differential equation into a representation that corresponds to a linear system of algebraic equations. Furthermore, we conduct a comparative analysis between the outcomes obtained from the suggested method and those derived from the rationalized Haar wavelet method without employing any shared mathematical methodologies. In order to evaluate the precision and effectiveness of the proposed method, a series of numerical examples have been developed.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"12 1","pages":"0"},"PeriodicalIF":3.6000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space\",\"authors\":\"Amnah E. Shammaky, Eslam M. Youssef, Mohamed A. Abdou, Mahmoud M. ElBorai, Wagdy G. ElSayed, Mai Taha\",\"doi\":\"10.3390/fractalfract7110796\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work aims to explore the solution of a nonlinear fractional integro-differential equation in the complex domain through the utilization of both analytical and numerical approaches. The demonstration of the existence and uniqueness of a solution is established under certain appropriate conditions with the use of Banach fixed point theorems. To date, no research effort has been undertaken to look into the solution of this integro equation, particularly due to its fractional order specification within the complex plane. The validation of the proposed methodology was performed by utilizing a novel strategy that involves implementing the Rationalized Haar wavelet numerical method with the application of the Bernoulli polynomial technique. The primary reason for choosing the proposed technique lies in its ability to transform the solution of the given nonlinear fractional integro-differential equation into a representation that corresponds to a linear system of algebraic equations. Furthermore, we conduct a comparative analysis between the outcomes obtained from the suggested method and those derived from the rationalized Haar wavelet method without employing any shared mathematical methodologies. In order to evaluate the precision and effectiveness of the proposed method, a series of numerical examples have been developed.\",\"PeriodicalId\":12435,\"journal\":{\"name\":\"Fractal and Fractional\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractal and Fractional\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/fractalfract7110796\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractal and Fractional","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/fractalfract7110796","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

摘要

本研究旨在利用解析和数值方法,探讨复域非线性分数阶积分微分方程的解法。利用Banach不动点定理,在一定条件下证明了解的存在唯一性。到目前为止,还没有研究工作来研究这个积分方程的解,特别是由于它在复平面内的分数阶规范。通过利用一种新的策略来验证所提出的方法,该策略涉及应用伯努利多项式技术实现合理化Haar小波数值方法。选择所提出的技术的主要原因在于它能够将给定的非线性分数阶积分微分方程的解转换为对应于线性代数方程组的表示。此外,我们在没有使用任何共享的数学方法的情况下,对所建议的方法得到的结果与从合理化Haar小波方法得到的结果进行了比较分析。为了验证所提方法的精度和有效性,给出了一系列数值算例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space
This work aims to explore the solution of a nonlinear fractional integro-differential equation in the complex domain through the utilization of both analytical and numerical approaches. The demonstration of the existence and uniqueness of a solution is established under certain appropriate conditions with the use of Banach fixed point theorems. To date, no research effort has been undertaken to look into the solution of this integro equation, particularly due to its fractional order specification within the complex plane. The validation of the proposed methodology was performed by utilizing a novel strategy that involves implementing the Rationalized Haar wavelet numerical method with the application of the Bernoulli polynomial technique. The primary reason for choosing the proposed technique lies in its ability to transform the solution of the given nonlinear fractional integro-differential equation into a representation that corresponds to a linear system of algebraic equations. Furthermore, we conduct a comparative analysis between the outcomes obtained from the suggested method and those derived from the rationalized Haar wavelet method without employing any shared mathematical methodologies. In order to evaluate the precision and effectiveness of the proposed method, a series of numerical examples have been developed.
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
Fractal and Fractional
Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
4.60
自引率
18.50%
发文量
632
审稿时长
11 weeks
期刊介绍: Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
期刊最新文献
On the Impacts of the Global Sea Level Dynamics Research on Application of Fractional Calculus Operator in Image Underlying Processing The Multiscale Principle in Nature (Principium luxuriæ): Linking Multiscale Thermodynamics to Living and Non-Living Complex Systems A Numerical Scheme and Application to the Fractional Integro-Differential Equation Using Fixed-Point Techniques Correction: Panchal et al. 3D FEM Simulation and Analysis of Fractal Electrode-Based FBAR Resonator for Tetrachloroethene (PCE) Gas Detection. Fractal Fract. 2022, 6, 491
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1