Fractional Corrected Simpson's Second Formula Type Inequalities via Extended s-Convexity

Abstract

In this paper, we establish new fractional variants of the corrected Simpson’s second formula type inequalities by leveraging the concept of extended s-convexity. To achieve this, we first derive a novel integral identity involving Riemann--Liouville fractional integrals, which serves as a fundamental auxiliary result. Building upon this identity, we obtain several inequalities for functions whose first-order derivatives satisfy the extended s-convexity condition on a given interval. Furthermore, we demonstrate the practical relevance of our theoretical findings by applying them to derive estimates for special means. These applications highlight the utility of our inequalities in numerical analysis and approximation theory.