Generalization of Some Fractional Integral Operator Inequalities for Convex Functions via Unified Mittag–Leffler Function

Abstract

This paper aims to obtain the bounds of a class of integral operators containing Mittag–Leffler functions in their kernels. A recently defined unified Mittag–Leffler function plays a vital role in connecting the results of this paper with the well-known bounds of fractional integral operators published in the recent past. The symmetry of a function about a line is a fascinating property that plays an important role in mathematical inequalities. A variant of the Hermite–Hadamard inequality is established using the closely symmetric property for (α,m)-convex functions.

Keywords

• integral operators
• fractional integral operators
• bounds
• (<i>α</i>,<i>m</i>)-convex function
• symmetry