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

Fractal and Fractional Pub Date : 2024-01-04 DOI:10.3390/fractalfract8010034

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。

查看原文本刊更多论文

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 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.