On generalization of different type inequalities for ({\alpha},m)-convex functions via fractional integrals

TL;DR

This paper introduces new fractional integral identities and derives generalized inequalities, including Hadamard, Ostrowski, and Simpson types, for functions with ({\alpha},m)-convex derivatives using Riemann-Liouville fractional integrals.

Contribution

It presents novel fractional integral identities and extends classical inequalities to ({\alpha},m)-convex functions, broadening their applicability.

Findings

Derived new fractional integral identities.

Established generalized inequalities for ({\alpha},m)-convex functions.

Unified several classical inequalities under a fractional integral framework.

Abstract

In this paper, new identity for fractional integrals have been defined. By using of this identity, we obtained new general inequalities containing all of Hadamard, Ostrowski and Simpson type inequalities for for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex via Riemann Liouville fractional integral.