On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>h</a:mi> </a:math>-Convex Functions
Xiaobin Wang, Muhammad Shoaib Saleem, Kiran Naseem Aslam, Xingxing Wu, Tong Zhou
Abstract
The theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mi>h</a:mi> </a:math> -convex function. We present some new Caputo–Fabrizio fractional estimates from Hermite–Hadamard-type inequalities. The results of this paper can be considered as the generalization and extension of many existing results of inequalities and convex functions. Moreover, we also present some application of our results to special means of real numbers.