On Bounds of <i>k</i>-Fractional Integral Operators with Mittag-Leffler Kernels for Several Types of Exponentially Convexities

Abstract

This paper aims to study the bounds of k-integral operators with the Mittag-Leffler kernel in a unified form. To achieve these bounds, the definition of exponentially (α,h−m)−p-convexity is utilized frequently. In addition, a fractional Hadamard type inequality which shows the upper and lower bounds of k-integral operators simultaneously is presented. The results are directly linked with the results of many published articles.

Keywords

• convex function
• exponentially (<i>α</i>, <i>h</i> − <i>m</i>)-<i>p</i>-convex function
• Mittag-Leffler function
• generalized integral operators