{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T01:04:34Z","timestamp":1775783074307,"version":"3.50.1"},"reference-count":106,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T00:00:00Z","timestamp":1690156800000},"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>A review of the results on the fractional Fej\u00e9r-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented. In the numerous families of convexities, it includes classical convex functions, s-convex functions, quasi-convex functions, strongly convex functions, harmonically convex functions, harmonically quasi-convex functions, quasi-geometrically convex functions, p-convex functions, convexity with respect to strictly monotone function, co-ordinated-convex functions, (\u03b8,h\u2212m)\u2212p-convex functions, and h-preinvex functions. Included in the fractional integral operators are Riemann\u2013Liouville fractional integral, (k\u2212p)-Riemann\u2013Liouville, k-Riemann\u2013Liouville fractional integral, Riemann\u2013Liouville fractional integrals with respect to another function, the weighted fractional integrals of a function with respect to another function, fractional integral operators with the exponential kernel, Hadamard fractional integral, Raina fractional integral operator, conformable integrals, non-conformable fractional integral, and Katugampola fractional integral. Finally, Fej\u00e9r-type fractional integral inequalities for invex functions and (p,q)-calculus are also included.<\/jats:p>","DOI":"10.3390\/axioms12070719","type":"journal-article","created":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T01:32:10Z","timestamp":1690248730000},"page":"719","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Comprehensive Review on the Fej\u00e9r-Type Inequality Pertaining to Fractional Integral Operators"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8372-2532","authenticated-orcid":false,"given":"Muhammad","family":"Tariq","sequence":"first","affiliation":[{"name":"Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro 76062, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3084-922X","authenticated-orcid":false,"given":"Asif Ali","family":"Shaikh","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro 76062, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1287\/moor.1110.0485","article-title":"Convex duality in stochastic optimization and mathematical finance","volume":"36","author":"Pennanen","year":"2011","journal-title":"Math. 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