Aldwoah Khaled, Shah Syed Khayyam, Hussain Sadam, Almalahi Mohammed A, Arko Yagoub A S, Hleili Manel
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medinah, Saudi Arabia.
Department of Mathematics, University of Malakand, Chakdara Dir(L), 18800, Khyber Pakhtunkhwa, Pakistan.
Sci Rep. 2024 Oct 9;14(1):23546. doi: 10.1038/s41598-024-74046-8.
The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized -contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of . Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of and and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.
不动点理论主要在两个方向上得到了推广。一个是空间的扩展，另一个是对压缩条件的放宽和推广。本文旨在在扩展的b - 度量空间的背景下建立有理型广义 - 压缩的新型不动点结果。鉴于 的特性，这将使我们能够在更宽松和多样的框架中分析广义有理型压缩。在这个方向上已经回顾了一些现有的有理型压缩，并定义了其他的。通过利用 和 的性质并应用迭代技术，建立了新的不动点结果。此外，所建立的结果被用于研究分形和分数阶微分方程以及电路的稳定性。为了所建立结果的可靠性，给出了积分包含系统和积分方程组的例子及应用。
