{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T23:43:18Z","timestamp":1778542998832,"version":"3.51.4"},"reference-count":21,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T00:00:00Z","timestamp":1684281600000},"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>In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two applications on Riemann\u2013Liouville fractional integrals and Atangana\u2013Baleanu fractional integrals.<\/jats:p>","DOI":"10.3390\/sym15051100","type":"journal-article","created":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T06:00:29Z","timestamp":1684389629000},"page":"1100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Controlled S-Metric-Type Spaces and Applications to Fractional Integrals"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0915-4909","authenticated-orcid":false,"given":"Nilay","family":"Ekiz Yazici","sequence":"first","affiliation":[{"name":"Departments of Mathematics, Bursa Technical University, Yildirim, Bursa 16310, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3877-2714","authenticated-orcid":false,"given":"Ozgur","family":"Ege","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ege University, Izmir 35100, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8798-3297","authenticated-orcid":false,"given":"Aiman","family":"Mukheimer","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operations dans les ensembles abstraits et leur application aux equations integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. 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