Available online at www.isr-publications.com/jmcs J. Math. Computer Sci., 19 (2019), 230–240 Research Article Online: ISSN 2008-949X Journal Homepage: www.isr-publications.com/jmcs Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for p-convex functions via new fractional conformable integral operators Naila Mehreen ∗ , Matloob Anwar School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan. Abstract In this paper, we obtained the Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for p-convex functions via new fractional conformable integral operators. We also gave some new Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for convex functions and harmonically convex functions via new fractional conformable integral operators. Keywords: Hermite-Hadamard inequalities, Hermite-Hadamard-Fejer inequalities, Riemann-Liouville fractional integral, fractional conformable integral operators, convex functions, p-convex functions, harmonically convex functions. 2010 MSC: 26A51, 26A33, 26D10, 26D07, 26D15. c 2019 All rights reserved. 1. Introduction A function ϕ : K → R on a real interval, for all k 1 , k 2 ∈ K and τ ∈ [0, 1], is called convex if ϕ(τk 1 +(1 - τ)k 2 )  τϕ(k 1 )+(1 - τ)ϕ(k 2 ) holds. Many authors gave results for convex functions due to its importance. The most well known inequality for convex functions is called The Hermite-Hadamard inequality [5] given as ϕ  k 1 + k 2 2   1 k 2 - k 1  k 2 k 1 ϕ(s)ds  ϕ(k 1 )+ ϕ(k 2 ) 2 , (1.1) where k 1 , k 2 ∈ K, k 1 <k 2 . Then Fejer [4] introduced the weighted generalization of (1.1) as follows ϕ  k 1 + k 2 2   k 2 k 1 g(s)ds  1 k 2 - k 1  k 2 k 1 ϕ(s)g(s)ds  ϕ(k 1 )+ ϕ(k 2 ) 2  k 2 k 1 g(s)ds, where g :[k 1 , k 2 ] → R is nonnegative, integrable, and symmetric to (k 1 + k 2 )/2. These two inequalities are then generalized in different ways. There are many generalization of convex functions. ∗ Corresponding author Email address: nailamehreen@gmail.com, naila.mehreen@sns.nust.edu.pk (Naila Mehreen) doi: 10.22436/jmcs.019.04.02 Received: 2018-06-02 Revised: 2018-11-23 Accepted: 2018-12-20