{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T19:51:40Z","timestamp":1775677900883,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T00:00:00Z","timestamp":1661385600000},"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>Fractional integrals and inequalities have recently become quite popular and have been the prime consideration for many studies. The results of many different types of inequalities have been studied by launching innovative analytical techniques and applications. These Hermite\u2013Hadamard inequalities are discovered in this study using Atangana\u2013Baleanu integral operators, which provide both practical and powerful results. In this paper, a symmetric study of integral inequalities of Hermite\u2013Hadamard type is provided based on an identity proved for Atangana\u2013Baleanu integral operators and using functions whose absolute value of the second derivative is harmonic convex. The proven Hermite\u2013Hadamard-type inequalities have been observed to be valid for a choice of any harmonic convex function with the help of examples. Moreover, fractional inequalities and their solutions are applied in many symmetrical domains.<\/jats:p>","DOI":"10.3390\/sym14091774","type":"journal-article","created":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T02:09:36Z","timestamp":1661911776000},"page":"1774","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Hermite\u2013Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana\u2013Baleanu Fractional Integral Operator"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2349-3445","authenticated-orcid":false,"given":"Muhammad Amer","family":"Latif","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, King Faisal University, Hofuf 31982, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5835-3349","authenticated-orcid":false,"given":"Humaira","family":"Kalsoom","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8567-0676","authenticated-orcid":false,"given":"Muhammad Zainul","family":"Abidin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.29229\/uzmj.2018-4-3","article-title":"New generalizations for functions whose second derivatives are GG-convex","volume":"4","author":"Akdemir","year":"2018","journal-title":"Uzbek Math. 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