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.