{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:15:56Z","timestamp":1760148956005,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,22]],"date-time":"2023-06-22T00:00:00Z","timestamp":1687392000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This manuscript contains several fixed point results for \u03b1\u0393-F-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that the distance function is consistent and does not favour any one direction in orthogonal fuzzy metric spaces. No matter how the points are arranged, it enables a fair assessment of the separations between all of them. In fixed point results, the symmetry condition is preserved for several types of contractive self-mappings. Moreover, we provide several non-trivial examples to show the validity of our main results. Furthermore, we solve non-linear fractional differential equations, the Atangana\u2013Baleanu fractional integral operator and Fredholm integral equations by utilizing our main results.<\/jats:p>","DOI":"10.3390\/sym15071300","type":"journal-article","created":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T01:54:56Z","timestamp":1687485296000},"page":"1300","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Development of Fixed Point Results for \u03b1\u0393-F-Fuzzy Contraction Mappings with Applications"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4303-2884","authenticated-orcid":false,"given":"Salvatore","family":"Sessa","sequence":"first","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 Dinapoli Federico II, Via Toledo 403, 80121 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fahad","family":"Jahangeer","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Doha A.","family":"Kattan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts, King Abdulaziz University, Rabigh 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5228-1073","authenticated-orcid":false,"given":"Umar","family":"Ishtiaq","sequence":"additional","affiliation":[{"name":"Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,22]]},"reference":[{"key":"ref_1","first-page":"338","article-title":"Information and control","volume":"8","author":"Zadeh","year":"1965","journal-title":"Fuzzy Sets"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"313","DOI":"10.2140\/pjm.1960.10.313","article-title":"Statistical metric spaces","volume":"10","author":"Schweizer","year":"1960","journal-title":"Pac. 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