SOME NEW INTEGRAL INEQUALITIES OF OSTROWSKI TYPE BY INCORPORATING THE ATANGANA–BALEANU FRACTIONAL INTEGRAL OPERATOR

The aim of this paper is to integrate the concept of Ostrowski inequality with the Atangana–Baleanu fractional integral operator. First, we derive an equality that involves the Atangana–Baleanu fractional integral operator. Next, using this equality, we introduce novel generalizations of Ostrowski-type inequalities by applying several key mathematical tools like Hölder’s inequality, the power-mean inequality, Young’s inequality, and the Jensen integral inequality all applied to the preinvexity of [Formula: see text]. Furthermore, several special cases are deduced from the main findings, contributing to the advancement of fractional calculus in the context of convexity and integral inequalities. These results offer potential applications in various fields where fractional calculus plays a significant role.