{"title":"New Contributions to Fixed Point Techniques with Applications for Solving Fractional and Differential Equations","authors":"Hasanen A. Hammad, Hassen Aydi, Doha A. Kattan","doi":"10.1007/s12346-023-00932-7","DOIUrl":null,"url":null,"abstract":"<p>In this article, we present two novel ideas of <i>f</i>-contractions, named dual <span>\\(f^{*}\\)</span>-weak rational contractions and triple <span>\\(f^{*}\\)</span>-weak rational contractions, generalizing and expanding many of the solid results in this direction. The endeavor to apply the generalized Banach contraction principle to the set of <i>f</i>-contraction type mappings by applying numerous <i>f</i>-type functions gave rise to these novel generalizations. Also, under appropriate conditions, related unique fixed-point theorems are established. Moreover, some illustrative examples are given to support and strengthen the theoretical results. Furthermore, the obtained results are applied to discuss the existence of solutions to a fractional integral equation and a second-order differential equation. Finally, the significance of the new results and some future work are presented.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"51 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Qualitative Theory of Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-023-00932-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we present two novel ideas of f-contractions, named dual \(f^{*}\)-weak rational contractions and triple \(f^{*}\)-weak rational contractions, generalizing and expanding many of the solid results in this direction. The endeavor to apply the generalized Banach contraction principle to the set of f-contraction type mappings by applying numerous f-type functions gave rise to these novel generalizations. Also, under appropriate conditions, related unique fixed-point theorems are established. Moreover, some illustrative examples are given to support and strengthen the theoretical results. Furthermore, the obtained results are applied to discuss the existence of solutions to a fractional integral equation and a second-order differential equation. Finally, the significance of the new results and some future work are presented.
在这篇文章中，我们提出了两种新的 f-收缩思想，分别命名为二重 \(f^{*}\)- 弱有理收缩和三重 \(f^{*}\)- 弱有理收缩，概括并扩展了这个方向上的许多可靠结果。通过应用众多 f 型函数，努力将广义巴拿赫收缩原理应用于 f 收缩类型映射集合，从而产生了这些新颖的广义。同时，在适当的条件下，建立了相关的唯一定点定理。此外，还给出了一些示例来支持和加强理论结果。此外，还将所得结果应用于讨论分数积分方程和二阶微分方程的解的存在性。最后，介绍了新结果的意义和未来的一些工作。
期刊介绍：
Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.
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