{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:07:21Z","timestamp":1760148441681,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSP2023R158"],"award-info":[{"award-number":["RSP2023R158"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function E\u03bc,\u03b1,l\u03b3,\u03b4,k,c(\u03c4;p) as a kernel in the interval domain. Additionally, a new form of Atangana\u2013Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in E\u03bc,\u03b1,l\u03b3,\u03b4,k,c(\u03c4;p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite\u2013Hadamard, Pachapatte, and Hermite\u2013Hadamard\u2013Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases.<\/jats:p>","DOI":"10.3390\/sym15051012","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T12:02:31Z","timestamp":1682942551000},"page":"1012","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Generalized AB-Fractional Operator Inclusions of Hermite\u2013Hadamard\u2019s Type via Fractional Integration"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2160-4159","authenticated-orcid":false,"given":"Bandar","family":"Bin-Mohsin","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1019-9485","authenticated-orcid":false,"given":"Muhammad","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5212-6252","authenticated-orcid":false,"given":"Muhammad","family":"Javed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Awais","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8843-955X","authenticated-orcid":false,"given":"H\u00fcseyin","family":"Budak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, Duzce 81620, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4864-8899","authenticated-orcid":false,"given":"Marcela","family":"Mihai","sequence":"additional","affiliation":[{"name":"Department Scientific-Methodical Sessions, Romanian Mathematical Society-Branch Bucharest, Academy Street no. 14, RO-010014 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6105-2435","authenticated-orcid":false,"given":"Muhammad","family":"Noor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 4000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,1]]},"reference":[{"key":"ref_1","unstructured":"Dragomir, S.S., and Pearce, C.E.M. 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