{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T19:18:38Z","timestamp":1773515918369,"version":"3.50.1"},"reference-count":65,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,7]],"date-time":"2023-05-07T00:00:00Z","timestamp":1683417600000},"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>The term convexity associated with the theory of inequality in the sense of fractional analysis has a broad range of different and remarkable applications in the domain of applied sciences. The prime objective of this article is to investigate some new variants of Hermite\u2013Hadamard and Pachpatte-type integral inequalities involving the idea of the preinvex function in the frame of a fractional integral operator, namely the Caputo\u2013Fabrizio fractional operator. By employing our approach, a new fractional integral identity that correlates with preinvex functions for first-order differentiable mappings is presented. Moreover, we derive some refinements of the Hermite\u2013Hadamard-type inequality for mappings, whose first-order derivatives are generalized preinvex functions in the Caputo\u2013Fabrizio fractional sense. From an application viewpoint, to represent the usability of the concerning results, we presented several inequalities by using special means of real numbers. Integral inequalities in association with convexity in the frame of fractional calculus have a strong relationship with symmetry. Our investigation provides a better image of convex analysis in the frame of fractional calculus.<\/jats:p>","DOI":"10.3390\/sym15051033","type":"journal-article","created":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T01:32:53Z","timestamp":1683509573000},"page":"1033","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some New Fractional Hadamard and Pachpatte-Type Inequalities with Applications via Generalized Preinvexity"],"prefix":"10.3390","volume":"15","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\/0000-0002-3084-922X","authenticated-orcid":false,"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\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Breaz, D., Yildiz, C., Cotirla, L.-I., Rahman, G., and Yerg\u00f6z, B. 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