Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for generalized fractional integrals

Abstract

In this paper we obtain the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for fractional integrals which generalize the two familiar fractional integrals namely, the Riemann–Liouville and the Hadamard fractional integrals into a single form. We prove that, in most cases, we obtain the Riemann–Liouville and the Hadamard equivalence just by taking limits when a parameter ρ→1 and ρ→0+, respectively.