Integral inequalities for some convex functions via generalized fractional integrals

In this paper, we obtain the Hermite-Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann-Liouville fractional integral and Hadamard fractional integral. We show that through the Katugampola fractional integral we can find a Hermite-Hadamard inequality via the Riemann-Liouville fractional integral.