Generalizations of Hermite–Hadamard like inequalities involving χ κ $\chi _{{\kappa }}$ -Hilfer fractional integrals

Abstract

Abstract The main objective of this paper is to obtain a new κ-fractional analogue of Hermite–Hadamard’s inequality using the class of s-convex functions and χ κ $\chi _{{\kappa }}$ -Hilfer fractional integrals. In order to obtain other main results of the paper we derive two new fractional integral identities using the definitions of χ κ $\chi _{{\kappa }}$ -Hilfer fractional integrals. For the validity of these identities we also take some particular examples. Using these identities we then obtain some more new variants of Hermite–Hadamard’s inequality using s-convex functions.

Keywords

• Convex
• s-convex
• Fractional
• Hilfer
• Hermite–Hadamard inequality