使用定点技术的数值方案及其在分数积分微分方程中的应用

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
A. Gnanaprakasam, Balaji Ramalingam, Gunaseelan Mani, Ozgur Ege, Reny George
{"title":"使用定点技术的数值方案及其在分数积分微分方程中的应用","authors":"A. Gnanaprakasam, Balaji Ramalingam, Gunaseelan Mani, Ozgur Ege, Reny George","doi":"10.3390/fractalfract8010034","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the notion of orthogonal α–F–convex contraction mapping and prove some fixed-point theorems for self-mapping in orthogonal complete metric spaces. The proven results generalize and extend some of the well-known results in the literature. Following the derivation of these fixed-point results, we propose a solution for the fractional integro-differential equation, utilizing the fixed-point technique within the context of orthogonal complete metric spaces.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"60 6","pages":""},"PeriodicalIF":3.6000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Numerical Scheme and Application to the Fractional Integro-Differential Equation Using Fixed-Point Techniques\",\"authors\":\"A. Gnanaprakasam, Balaji Ramalingam, Gunaseelan Mani, Ozgur Ege, Reny George\",\"doi\":\"10.3390/fractalfract8010034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce the notion of orthogonal α–F–convex contraction mapping and prove some fixed-point theorems for self-mapping in orthogonal complete metric spaces. The proven results generalize and extend some of the well-known results in the literature. Following the derivation of these fixed-point results, we propose a solution for the fractional integro-differential equation, utilizing the fixed-point technique within the context of orthogonal complete metric spaces.\",\"PeriodicalId\":12435,\"journal\":{\"name\":\"Fractal and Fractional\",\"volume\":\"60 6\",\"pages\":\"\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2024-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractal and Fractional\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3390/fractalfract8010034\",\"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":"100","ListUrlMain":"https://doi.org/10.3390/fractalfract8010034","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

本文介绍了正交α-F-凸收缩映射的概念,并证明了正交完全度量空间中自映射的一些定点定理。所证明的结果概括并扩展了文献中的一些著名结果。在推导出这些定点结果之后,我们在正交完全度量空间的背景下利用定点技术提出了分数积分微分方程的解决方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Numerical Scheme and Application to the Fractional Integro-Differential Equation Using Fixed-Point Techniques
In this paper, we introduce the notion of orthogonal α–F–convex contraction mapping and prove some fixed-point theorems for self-mapping in orthogonal complete metric spaces. The proven results generalize and extend some of the well-known results in the literature. Following the derivation of these fixed-point results, we propose a solution for the fractional integro-differential equation, utilizing the fixed-point technique within the context of orthogonal complete metric spaces.
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.
×
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