{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T12:51:34Z","timestamp":1765889494492,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T00:00:00Z","timestamp":1746748800000},"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>In this study, we introduce a new hybrid identity that effectively combines Newton\u2013Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson\u2019s second rule and the left- and right-Radau two-point rules, among others. Building upon this flexible framework, we establish several new biparametrized fractal integral inequalities for functions whose local fractional derivatives are of a generalized convex type. In addition to employing tools from local fractional calculus, our approach utilizes the H\u00f6lder inequality, the power mean inequality, and a refined version of the latter. Further results are also derived using the concept of generalized concavity. To support our theoretical findings, we provide a graphical example that illustrates the validity of the obtained results, along with some practical applications that demonstrate their effectiveness.<\/jats:p>","DOI":"10.3390\/axioms14050358","type":"journal-article","created":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T11:25:53Z","timestamp":1746789953000},"page":"358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hybrid Integral Inequalities on Fractal Set"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0156-7864","authenticated-orcid":false,"given":"Badreddine","family":"Meftah","sequence":"first","affiliation":[{"name":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Facuty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0600-2624","authenticated-orcid":false,"given":"Wedad","family":"Saleh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 42210, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1019-9485","authenticated-orcid":false,"given":"Muhammad Uzair","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1234-7939","authenticated-orcid":false,"given":"Loredana","family":"Ciurdariu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2943-2678","authenticated-orcid":false,"given":"Abdelghani","family":"Lakhdari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, T\u00fcrkiye"},{"name":"Laboratory of Energy Systems Technology, Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,9]]},"reference":[{"key":"ref_1","unstructured":"Pe\u010dari\u0107, J.E., Proschan, F., and Tong, Y.L. 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