On the Hermite–Hadamard type inequality for ψ-Riemann–Liouville fractional integrals via convex functions

Abstract

Abstract In this paper, we establish a new Hermite–Hadamard inequality involving left-sided and right-sided ψ-Riemann–Liouville fractional integrals via convex functions. We also show two basic ψ-Riemann–Liouville fractional integral identities including the first order derivative of a given convex function, and these will be used to derive estimates for some fractional Hermite–Hadamard inequalities. Finally, we give some applications to special means of real numbers.

Keywords

• Hermite–Hadamard inequality
• ψ-Riemann–Liouville fractional integrals