{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:50:06Z","timestamp":1760057406085,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T00:00:00Z","timestamp":1738713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Fixed-point theory plays a pivotal role in addressing equations that model various real-life applications, offering robust methods to find solutions that remain stable under different conditions and dynamics. The main objective of this paper is to introduce and study the novel concept of probabilistic F-contraction within the framework of Menger spaces. This innovative approach extends classical fixed-point results to probabilistic settings, leveraging the probabilistic structure of Menger spaces to handle uncertainty and variability in the modeling process. By establishing the existence and uniqueness of fixed points in this versatile class of spaces, the study highlights the broader applicability and deeper significance of the probabilistic F-contraction. We explore the intricate interrelations among these fixed points, shedding light on their implications across different contexts and presenting insights into various theorem versions that enhance our understanding of their utility. Additionally, we propose a straightforward and effective approach for solving a system of Fredholm integral equations using fixed-point techniques specifically tailored for Menger spaces, illustrating their practical utility in tackling the complex mathematical models encountered in diverse fields.<\/jats:p>","DOI":"10.3390\/axioms14020119","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T04:15:41Z","timestamp":1738728941000},"page":"119","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Solving Fredholm Integral Equations Using Probabilistic F-Contractions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7723-3721","authenticated-orcid":false,"given":"Ismail","family":"Tahiri","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Normal Higher School, Abdelmalek Essaadi University, Martil, Tetouan P.O. Box 209, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5334-2383","authenticated-orcid":false,"given":"Youssef","family":"Achtoun","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Normal Higher School, Abdelmalek Essaadi University, Martil, Tetouan P.O. Box 209, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8270-2660","authenticated-orcid":false,"given":"Mohammed","family":"Lamarti Sefian","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Normal Higher School, Abdelmalek Essaadi University, Martil, Tetouan P.O. Box 209, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8254-6688","authenticated-orcid":false,"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Beograd 35, 11120 Beograd, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s13398-020-00877-5","article-title":"F-contraction mappings on metric-like spaces in connection with integral equations on time scales","volume":"114","author":"Agarwal","year":"2020","journal-title":"Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. 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