Fractional integral inequalities of Hermite-Hadamard type for convex functions with respect to a monotone function

Abstract

In the literature, the left-side of Hermite--Hadamard's inequality is called a midpoint type inequality. In this article, we obtain new integral inequalities of midpoint type for Riemann--Liouville fractional integrals of convex functions with respect to increasing functions. The resulting inequalities generalize some recent classical integral inequalities and Riemann--Liouville fractional integral inequalities established in earlier works. Finally, applications of our work are demonstrated via the known special functions of real numbers.