Exploring Milne-Type Inequalities through the Generalized Riemann-Liouville Fractional Operator

Abstract

This study investigates the bounds for one of the open Newton-Cotes formula, known as Milne's formula for the differentiable convex functions within the framework of recently defined generalized Riemann-Liouville $(k, p)$-fractional integral operators. Some novel inequalities of Milne-type are deduced for the differentiable functions using the well known H\"{o}lder, power-mean and some other relevant inequalities.To substantiate our theoretical findings, we present illustrative examples accompanied by graphical representations that effectively demonstrate the practical implications of the established inequalities. The results validate our theoretical framework and underscore the applicability of these inequalities across various contexts.