{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T10:54:52Z","timestamp":1762080892126,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T00:00:00Z","timestamp":1671062400000},"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 paper, we shall discuss a newly introduced concept of center-radius total-ordered relations between two intervals. Here, we address the Hermite\u2013Hadamard-, Fej\u00e9r- and Pachpatte-type inequalities by considering interval-valued Riemann\u2013Liouville fractional integrals. Interval-valued fractional inequalities for a new class of preinvexity, i.e., cr-h-preinvexity, are estimated. The fractional operator is used for the first time to prove such inequalities involving center\u2013radius-ordered functions. Some numerical examples are also provided to validate the presented inequalities.<\/jats:p>","DOI":"10.3390\/axioms11120732","type":"journal-article","created":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T03:01:51Z","timestamp":1671073311000},"page":"732","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Modified Inequalities on Center-Radius Order Interval-Valued Functions Pertaining to Riemann\u2013Liouville Fractional Integrals"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4524-1951","authenticated-orcid":false,"given":"Soubhagya Kumar","family":"Sahoo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Institute of Technical Education and Research, Siksha \u2018O\u2019 Anusandhan University, Bhubaneswar 751030, Odisha, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0223-4711","authenticated-orcid":false,"given":"Eman","family":"Al-Sarairah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates"},{"name":"Department of Mathematics, Al-Hussein Bin Talal University, Ma\u2019an P.O. Box 33011, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8372-2532","authenticated-orcid":false,"given":"Muhammad","family":"Tariq","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7469-5402","authenticated-orcid":false,"given":"Kamsing","family":"Nonlaopon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,15]]},"reference":[{"key":"ref_1","first-page":"171","article-title":"\u00c9tude sur les propri\u00e9t\u00e9s des fonctions enti\u00e9res en particulier d\u2019une fonction consid\u00e9r\u00e9\u00e9 par Riemann","volume":"58","author":"Hadamard","year":"1893","journal-title":"J. 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