Revisiting the Hermite-Hadamard fractional integral inequality via a Green function

Abstract

The Hermite-Hadamard inequality by means of the Riemann-Liouville fractional integral operators is already known in the literature. In this paper, it is our purpose to reconstruct this inequality via a relatively new method called the green function technique. In the process, some identities are established. Using these identities, we obtain loads of new results for functions whose second derivative is convex, monotone and concave in absolute value. We anticipate that the method outlined in this article will stimulate further investigation in this direction.