Several Integral Inequalities of Hermite–Hadamard Type Related to <i>k</i>-Fractional Conformable Integral Operators

Abstract

In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of Hermite–Hadamard type via Hölder’s inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact.

Keywords

• convexity
• <i>k</i>-gamma function
• Riemann–Liouville fractional integral
• conformable integral
• <i>k</i>-fractional conformable integral
• E-beta functions