Examining the Hermite–Hadamard Inequalities for <i>k</i>-Fractional Operators Using the Green Function

Abstract

For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities for k-Riemann–Liouville fractional integral operators by using a novel method based on Green’s function. Additionally, applying these identities to the convex and monotone functions, new Hermite–Hadamard type inequalities are established. Furthermore, a different form of the Hermite–Hadamard inequality is also obtained by using this novel approach. In conclusion, we believe that the approach presented in this paper will inspire more research in this area.

Keywords

• Hermite–Hadamard inequality
• convex functions
• green functions
• <i>k</i>-Riemann–Liouville fractional operators