Fractional integral inequalities via Atangana-Baleanu operators for convex and concave functions

TL;DR

This paper introduces new fractional integral inequalities using Atangana-Baleanu operators for convex and concave functions, expanding the mathematical tools available for fractional calculus analysis.

Contribution

It presents a novel identity involving Atangana-Baleanu fractional integrals and derives new inequalities for convex and concave functions.

Findings

Established a new identity with Atangana-Baleanu fractional integrals

Derived new fractional integral inequalities for convex functions

Derived new fractional integral inequalities for concave functions

Abstract

Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu in [2]. In this study, firstly, a new identity by using Atangana-Baleanu fractional integral operators are proved. Then, new fractional integral inequalities have been obtained for convex and concave functions with the help of this identity and some certain integral inequalities