{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:31:40Z","timestamp":1772253100092,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,5]],"date-time":"2020-04-05T00:00:00Z","timestamp":1586044800000},"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, a new identity for the generalized fractional integral is defined. Using this identity we studied a new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. This fractional integral generalizes Riemann-Liouville and Hadamard\u2019s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality.<\/jats:p>","DOI":"10.3390\/sym12040568","type":"journal-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T03:40:19Z","timestamp":1586403619000},"page":"568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals"],"prefix":"10.3390","volume":"12","author":[{"given":"Ohud","family":"Almutairi","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1217-963X","authenticated-orcid":false,"given":"Adem","family":"K\u0131l\u0131\u00e7man","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Institite for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,5]]},"reference":[{"key":"ref_1","unstructured":"Peajcariaac, J.E., and Tong, Y.L. 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