Fractional generalized Hadamard and Fejér-Hadamard inequalities for m-convex functions

Abstract

The objective of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities in generalized forms. By employing a generalized fractional integral operator containing extended generalized Mittag-Leffler function involving a monotone increasing function, we generalize the well known fractional Hadamard and Fejér-Hadamard inequalities for m-convex functions. Also we study the error bounds of these generalized inequalities. In connection with some published results from presented inequalities are obtained.

Keywords

• m-convex function
• fractional integral inequalities
• generalized fractional integral operator
• extended generalized mittag-leffler function