Hermite-Hadamard and Hermite-Hadamard-Fej\'er type Inequalities for Generalized Fractional Integrals

摘要

In this paper we obtain the Hermite-Hadamard and Hermite-Hadamard-Fej\'ertype inequalities for fractional integrals which generalize the two familiarfractional integrals namely, the Riemann-Liouville and the Hadamard fractionalintegrals into a single form. We prove that, in most cases, we obtain theRiemann--Liouville and the Hadamard equivalence just by taking limits when aparameter $\rho \rightarrow 1$ and $\rho \rightarrow 0^+$, respectively.