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

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.