{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T04:18:36Z","timestamp":1773029916127,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,9]],"date-time":"2020-09-09T00:00:00Z","timestamp":1599609600000},"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 integral inequality plays a significant role in pure and applied mathematics fields. It aims to develop and extend various mathematical methods. Therefore, nowadays we need to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of the fractional methods. Besides, the convexity theory plays a concrete role in the field of fractional integral inequalities due to the behavior of its definition and properties. There is also a strong relationship between convexity and symmetric theories. So, whichever one we work on, we can then apply it to the other one due to the strong correlation produced between them, specifically in the last few decades. First, we recall the definition of \u03c6-Riemann\u2013Liouville fractional integral operators and the recently defined class of convex functions, namely the \u03c3\u02d8-convex functions. Based on these, we will obtain few integral inequalities of Hermite\u2013Hadamard\u2019s type for a \u03c3\u02d8-convex function with respect to an increasing function involving the \u03c6-Riemann\u2013Liouville fractional integral operator. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann\u2013Liouville fractional integral inequalities. Finally, application to certain special functions are pointed out.<\/jats:p>","DOI":"10.3390\/sym12091485","type":"journal-article","created":{"date-parts":[[2020,9,10]],"date-time":"2020-09-10T22:58:01Z","timestamp":1599778681000},"page":"1485","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Fractional Hermite-Hadamard Integral Inequalities for a New Class of Convex Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8889-3768","authenticated-orcid":false,"given":"Thabet","family":"Abdeljawad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia"},{"name":"Department of Medical Research, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Computer Science and Information Engineering, Asia University, Taichung 41354, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1818-842X","authenticated-orcid":false,"given":"Shengda","family":"Zeng","sequence":"additional","affiliation":[{"name":"Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30348 Krakow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0115-3079","authenticated-orcid":false,"given":"Artion","family":"Kashuri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora 9401, Albania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,9]]},"reference":[{"key":"ref_1","first-page":"33","article-title":"On some Ostrowski type inequalities","volume":"18","author":"Gavrea","year":"2010","journal-title":"Gen. Math."},{"key":"ref_2","first-page":"1936461","article-title":"Simpson\u2019s Integral Inequalities for Twice Differentiable Convex Functions","volume":"2020","author":"Abdeljawad","year":"2020","journal-title":"Math. Probl. 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