Hermite-Hadamard type inequalities pertaining conformable fractional integrals and their applications

Abstract

In this paper, our main aim is to give results for conformable fractional integral version of Hermite-Hadamard inequality and their applications for mid-point formula and means. First, we prove an identity associated with the Hermite-Hadamard inequality for conformable fractional integrals. By using this identity and convexity of different classes of functions and some well-known inequalities, we obtain several results for the inequality. At the end, we also present applications for some error estimations of the mid-point formula and means. The results obtained in this paper generalize the earlier results. Furthermore, the identity can be used to obtain results for Hermite-Hadamard inequality for some other generalized classes of convex functions.