{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T10:45:13Z","timestamp":1777373113355,"version":"3.51.4"},"reference-count":56,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T00:00:00Z","timestamp":1644192000000},"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>In this paper, we discuss the Riemann\u2013Liouville fractional integral operator for left and right convex interval-valued functions (left and right convex I\u2219V-F), as well as various related notions and concepts. First, the authors used the Riemann\u2013Liouville fractional integral to prove Hermite\u2013Hadamard type (\ud835\udcd7\u2013\ud835\udcd7 type) inequality. Furthermore, \ud835\udcd7\u2013\ud835\udcd7 type inequalities for the product of two left and right convex I\u2219V-Fs have been established. Finally, for left and right convex I\u2219V-Fs, we found the Riemann\u2013Liouville fractional integral Hermite\u2013Hadamard type inequality (\ud835\udcd7\u2013\ud835\udcd7 Fej\u00e9r type inequality). The findings of this research show that this methodology may be applied directly and is computationally simple and precise.<\/jats:p>","DOI":"10.3390\/sym14020341","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T20:36:42Z","timestamp":1644266202000},"page":"341","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Fractional Calculus for Convex Functions in Interval-Valued Settings and Inequalities"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7450-8067","authenticated-orcid":false,"given":"Muhammad Bilal","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hatim Ghazi","family":"Zaini","sequence":"additional","affiliation":[{"name":"Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8209-3869","authenticated-orcid":false,"given":"Savin","family":"Trean\u021b\u01ce","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6609-5493","authenticated-orcid":false,"given":"Gustavo","family":"Santos-Garc\u00eda","sequence":"additional","affiliation":[{"name":"Facultad de Econom\u00eda y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7580-7533","authenticated-orcid":false,"given":"Jorge E.","family":"Mac\u00edas-D\u00edaz","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y F\u00edsica, Universidad Aut\u00f3noma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico"},{"name":"Department of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9431-4195","authenticated-orcid":false,"given":"Mohamed S.","family":"Soliman","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Niculescu, C.P., and Persson, L.E. (2006). Convex Functions and Their Applications, Springer.","DOI":"10.1007\/0-387-31077-0"},{"key":"ref_2","first-page":"171","article-title":"\u00c9tude sur les Propri\u00e9t\u00e9s des Fonctions Enti\u00e8res en Particulier d\u2019une Fonction Consid\u00e9r\u00e9e par Riemann","volume":"58","author":"Hadamard","year":"1893","journal-title":"J. Math. Pures. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1016\/j.aml.2010.04.037","article-title":"On Some Inequalities of Hermite-Hadamard Type via M-Convexity","volume":"23","author":"Avci","year":"2010","journal-title":"Appl. Math. 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