Hermite-Hadamard Fractional Integral Inequalities via Abel-Gontscharoff Green's Function

The Hermite-Hadamard inequalities for K-Riemann-Liouville fractional integrals (R-LFI) are presented in this study using a relatively novel approach based on Abel-Gontscharoff Green's function. In this new technique, we first established some integral identities. Such identities are used to obtain new results for monotonic functions whose second derivative is convex (concave) in absolute value. Some previously published inequalities are obtained as special cases of our main results. Various applications of our main consequences are also explored to special means and trapezoid-type formulae.

Automated summary

In this study, the Hermite-Hadamard inequalities for K-Riemann-Liouville fractional integrals are presented using an innovative approach based on Abel-Gontscharoff Green's function. By establishing integral identities, new results for monotonic functions with convex (concave) absolute second derivative are obtained. Some previously published inequalities are found to be special cases of the main results. Various applications of the main consequences, including special means and trapezoid-type formulae, are also explored.