{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T04:46:20Z","timestamp":1761108380567,"version":"3.41.2"},"reference-count":36,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T00:00:00Z","timestamp":1630886400000},"content-version":"vor","delay-in-days":248,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In this paper, authors prove new variants of Hermite\u2013Jensen\u2013Mercer type inequalities using <jats:italic>\u03c8<\/jats:italic>\u2013Riemann\u2013Liouville fractional integrals with respect to another function via convexity. We establish generalized identities involving <jats:italic>\u03c8<\/jats:italic>\u2013Riemann\u2013Liouville fractional integral pertaining first and twice differentiable convex function <jats:italic>\u03bb<\/jats:italic>, and these will be used to derive novel estimates for some fractional Hermite\u2013Jensen\u2013Mercer type inequalities. Some known results are recaptured from our results as special cases. Finally, an application from our results using the modified Bessel function of the first kind is established as well.<\/jats:p>","DOI":"10.1155\/2021\/9260828","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T20:23:16Z","timestamp":1630959796000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Fractional Hermite\u2013Jensen\u2013Mercer Integral Inequalities with respect to Another Function and Application"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7192-8269","authenticated-orcid":false,"given":"Saad Ihsan","family":"Butt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9911-1111","authenticated-orcid":false,"given":"Muhammad","family":"Umar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3468-2295","authenticated-orcid":false,"given":"Khuram Ali","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0115-3079","authenticated-orcid":false,"given":"Artion","family":"Kashuri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8034-1475","authenticated-orcid":false,"given":"Homan","family":"Emadifar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,9,6]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1142\/9789812817747_0002"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.3390\/axioms10020051"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-6042-7"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40096-016-0198-5"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym11121448"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-020-02955-9"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.3390\/math7100956"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-020-03093-y"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2020334"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-020-02693-y"},{"key":"e_1_2_8_11_2","first-page":"1","volume-title":"Classical and New Inequalities in Analysis","author":"Pe\u010dari\u0107 J.","year":"1993"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6944"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6869"},{"key":"e_1_2_8_14_2","first-page":"249","article-title":"Generalizations of cyclic refinements of Jensen\u2019s inequality by Lidstone\u2019s polynomial with applications in information theory","volume":"14","author":"Mehmood N.","year":"2019","journal-title":"Journal of Mathematical Inequalities"},{"key":"e_1_2_8_15_2","article-title":"A variant of Jensen\u2019s inequality","volume":"4","author":"Mercer A. 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