Exploring generalized Ostrowski-type inequalities through preinvex functions in fractional calculus

Abstract

This article presents a novel concept of pre-invex functions linked to generalized Ostrowski-type inequalities. We explore the integral representation of these pre-invex functions within the framework of local fractional calculus. This approach extends traditional calculus to analyze fractional-order derivatives and integrals. We establish several generalized Ostrowski-type inequalities by employing the properties of pre-invex functions and their representations as integrals. Several generalized Ostrowski-type inequalities are derived by employing the properties of pre-invex functions and their integral representation. These inequalities applied to the twice differentiable functions in the context of fractional calculus locally, allowing for a deeper understanding of their behaviors and applications. Our work contributes to the growing body of knowledge in this area by providing new insights and results that can be applied in various mathematical and applied fields.