{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T18:24:52Z","timestamp":1776191092946,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Deanship at University of Ha\u2019il\u2014Saudi Arabia","award":["RG-21021"],"award-info":[{"award-number":["RG-21021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Multiplicative calculus, also called non-Newtonian calculus, represents an alternative approach to the usual calculus of Newton (1643\u20131727) and Leibniz (1646\u20131716). This type of calculus was first introduced by Grossman and Katz and it provides a defined calculation, from the start, for positive real numbers only. In this investigation, we propose to study symmetrical fractional multiplicative inequalities of the Simpson type. For this, we first establish a new fractional identity for multiplicatively differentiable functions. Based on that identity, we derive new Simpson-type inequalities for multiplicatively convex functions via fractional integral operators. We finish the study by providing some applications to analytic inequalities.<\/jats:p>","DOI":"10.3390\/sym15020460","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T02:32:07Z","timestamp":1675909927000},"page":"460","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Multiplicatively Simpson Type Inequalities via Fractional Integral"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1080-3686","authenticated-orcid":false,"given":"Abdelkader","family":"Moumen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamid","family":"Boulares","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Department of Mathematics, Faculty MISM, 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, Department of Mathematics, Faculty MISM, University of Guelma, Guelma 24000, Algeria"}],"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":"Tariq","family":"Alraqad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, 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 Sciences, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zennir","family":"Khaled","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences and Arts, Qassim University, Ar Rass 58892, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"key":"ref_1","unstructured":"Grossman, M., and Katz, R. 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