应用于分数微分方程的临近点理论的最新进展

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-13 DOI:10.3390/axioms13060395

N. Mlaiki, Dur-e-Shehwar Sagheer, Sana Noreen, S. Batul, A. Aloqaily

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引用次数: 0

摘要

本文利用达留什-瓦尔道夫斯基（Dariusz Wardowski）提出的 F 收缩思想，在 b 度量空间的背景下介绍了广义（ﬀF,b,j˘）收缩的概念。研究的主要发现集中于部分有序 b-metric空间中多值（ﬀF,b,j˘）收缩的最佳邻近点的存在。文章举例说明了主要结果，并利用已建立的定理证明了二阶微分方程和分数微分方程解的存在性。此外，文章还提出了几个推论，说明这些结果概括了许多现有的定点定理和最佳邻近点定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Recent Advances in Proximity Point Theory Applied to Fractional Differential Equations

This article introduces the concept of generalized (ﬀF,b,ϕ˘) contraction in the context of b-metric spaces by utilizing the idea of F contraction introduced by Dariusz Wardowski. The main findings of the research focus on the existence of best proximity points for multi-valued (ﬀF,b,ϕ˘) contractions in partially ordered b-metric spaces. The article provides examples to illustrate the main results and demonstrates the existence of solutions to a second-order differential equation and a fractional differential equation using the established theorems. Additionally, several corollaries are presented to show that the results generalize many existing fixed-point and best proximity point theorems.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.