Some Estimates of <i>k</i>-Fractional Integrals for Various Kinds of Exponentially Convex Functions

Abstract

In this paper, we aim to find unified estimates of fractional integrals involving Mittag–Leffler functions in kernels. The results obtained in terms of fractional integral inequalities are provided for various kinds of convex and related functions. A variant of Hadamard-type inequality is also presented, which shows the upper and lower bounds of fractional integral operators of many kinds. The results of this paper are directly linked with many recently published inequalities.

Keywords

• convex function
• exponentially convex function
• Mittag–Leffler function
• fractional integral operators