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 $\rho \to 1$ and $\rho \to 0^{+}$, respectively.

Accepted Manuscript. 14 pages, Journal of Mathematical Analysis and Applications (2016)

References in corpus (2)

• Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals
• Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

Cited by in corpus (1)

• New fractional integral unifying six existing fractional integrals