{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:25:03Z","timestamp":1760235903089,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T00:00:00Z","timestamp":1633392000000},"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>In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of Hermite\u2013Hadamard type via H\u00f6lder\u2019s inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact.<\/jats:p>","DOI":"10.3390\/sym13101880","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1880","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Several Integral Inequalities of Hermite\u2013Hadamard Type Related to k-Fractional Conformable Integral Operators"],"prefix":"10.3390","volume":"13","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, Odisha, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5438-5407","authenticated-orcid":false,"given":"Hijaz","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II 39, 00186 Roma, Italy"},{"name":"Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]},{"given":"Jarunee","family":"Soontharanon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Niculescu, C.P., and Persson, L.E. 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