Hermite–Hadamard-type inequalities for Riemann–Liouville fractional integrals via two kinds of convexity

Abstract

In this article, two fundamental integral identities including the second-order derivatives of a given function via Riemann–Liouville fractional integrals are established. With the help of these two fractional-type integral identities, all kinds of Hermite–Hadamard-type inequalities involving left-sided and right-sided Riemann–Liouville fractional integrals for m-convex and (s, m)-convex functions, respectively. Our methods considered here may be a stimulant for further investigations concerning Hermite–Hadamard-type inequalities involving Hadamard fractional integrals.