Some New Milne-Type Inequalities via Katugampola Fractional Integrals

Abstract

Drawing inspiration from the findings presented in references \cite{9} and \cite{13}, this study aims to broaden the scope of Milne-type inequalities within the context of Katugampola fractional integrals, thus enriching the toolbox of fractional calculus. Through the discovery of a novel integral identity, we establish a suite of Milne-type inequalities tailored for functions whose first-order derivatives are $s$-convex in the second sense. To validate our theoretical advances, an example is provided, complete with graphical illustrations. The research concludes by underscoring the practical utility of these inequalities, showcasing their applicability across a wide range of fields within mathematical and applied sciences.