{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:11:04Z","timestamp":1760231464279,"version":"build-2065373602"},"reference-count":72,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T00:00:00Z","timestamp":1663632000000},"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 derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction of new fractional operators has prompted another direction in different branches of mathematics and applied sciences. First, we investigate and prove new fractional equality. Considering this equality as the auxiliary result, we attain some estimations of a Hermite\u2013Hadamard type inequality involving s-preinvex, s-Godunova\u2013Levin preinvex, and prequasi invex functions. In addition, we investigate a fractional order Hadamard\u2013Fej\u00e9r inequality and some of its refinements pertaining to h-preinvexity via a non-conformable fractional integral operator. Finally, we present a Pachpatte type inequality for the product of two preinvex functions. The findings as well as the special cases presented in this research are new and applications of our main results.<\/jats:p>","DOI":"10.3390\/sym14101957","type":"journal-article","created":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T00:08:09Z","timestamp":1663718889000},"page":"1957","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Some Hermite\u2013Hadamard and Hermite\u2013Hadamard\u2013Fej\u00e9r Type Fractional Inclusions Pertaining to Different Kinds of Generalized Preinvexities"],"prefix":"10.3390","volume":"14","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 University of Engineering and Technology, Jamshoro 76062, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4524-1951","authenticated-orcid":false,"given":"Soubhagya Kumar","family":"Sahoo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India"},{"name":"Department of Mathematics, Aryan Institute of Engineering and Technology, Bhubaneswar 752050, India"}]},{"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"},{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7530-6264","authenticated-orcid":false,"given":"Omar Mutab","family":"Alsalami","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia"}]},{"given":"Asif Ali","family":"Shaikh","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/S1573-4382(81)01005-9","article-title":"Mathematical analysis and convexity with applications to economics","volume":"1","author":"Green","year":"1981","journal-title":"Handb. 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