{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T00:03:00Z","timestamp":1779062580167,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:00:00Z","timestamp":1675814400000},"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>Various scholars have lately employed a wide range of strategies to resolve specific types of symmetrical fractional differential equations. In this paper, we propose a new fractional identity for multiplicatively differentiable functions; based on this identity, we establish some new fractional multiplicative Bullen-type inequalities for multiplicative differentiable convex functions. Some applications of the obtained results are given.<\/jats:p>","DOI":"10.3390\/sym15020451","type":"journal-article","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T03:57:16Z","timestamp":1675828636000},"page":"451","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Fractional Multiplicative Bullen-Type Inequalities for Multiplicative Differentiable Functions"],"prefix":"10.3390","volume":"15","author":[{"given":"Hamid","family":"Boulares","sequence":"first","affiliation":[{"name":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Badreddine","family":"Meftah","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1080-3686","authenticated-orcid":false,"given":"Abdelkader","family":"Moumen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3610-339X","authenticated-orcid":false,"given":"Ramsha","family":"Shafqat","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Lahore, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hicham","family":"Saber","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tariq","family":"Alraqad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5477-0065","authenticated-orcid":false,"given":"Ekram E.","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,8]]},"reference":[{"key":"ref_1","first-page":"325","article-title":"Milne type inequalities for differentiable s-convex functions","volume":"44","author":"Djenaoui","year":"2022","journal-title":"Honam Math. 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