On generalization of different type inequalities for some convex functions via fractional integrals

TL;DR

This paper introduces new identities for fractional integrals and uses them to derive generalized inequalities of Hadamard, Ostrowski, and Simpson types for various convex functions, expanding the theoretical framework of fractional calculus.

Contribution

It presents novel identities for fractional integrals and extends classical inequalities to broader classes of convex functions using these identities.

Findings

New identities for fractional integrals established

Generalized inequalities for s-convex, quasi-convex, m-convex functions derived

Enhanced bounds for classical inequalities via fractional calculus

Abstract

New identity for fractional integrals have been defined. By using of this identity, we obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for s-convex, quasi-convex, m-convex functions via Riemann Liouville fractional integral.