eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2022-08-03 10 1 15 20 10.12691/tjant-10-1-4 TJANT20221014 article Muhammad Muddassar malik.muddassar@gmail.com 1 Sajida Batool 1 Tahira Jabeen 2 Department of Basic Sciences, University of Engineering & Technology Taxila Department of Mathematics & Statistics, International Islamic University Islamabad In the paper under consideration, we will discuss integral inequalities by the way of fractional integral operators for generalized convex functions. For fractional integral operators, a new identity is established and some results of Hermite-Hadamard type inequalities are achieved. This fractional operator have been used to derive a new generalization of the Hermite-Hadamard inequality. In the previous papers the author used the definition of k-fractional conformable integral inequalities and we used the definition of katugampola fractional integrals in this paper. In this paper, we have given a best appropriate definition for fractional integral operators. http://pubs.sciepub.com/tjant/10/1/4/tjant-10-1-4.pdf Hermite-Hadamard inequality Katugampola fractional integrals generalized convex function