On the generalization of Hermite-Hadamard type inequalities for -convex function via fractional integrals.

The main motivation in this article is to prove new integral identities and related results. In this paper, we deal with -convex function, Hermite-Hadamard type inequalities, and Katugampola fractional integrals. Firstly, we established the Hermite-Hadamard type inequalities for -convex function via Katugampola fractional integrals operators. After that we obtain several new identities and give new results of Holder's inequality, Jensen's integral inequality, Young's inequality, and Power mean inequality for -convex function by using Katugampola fractional integral operators. We make connections of our results with various results recognized in the literature.