On Some Milne–Mercer-Type Inequalities via Atangana–Baleanu Conformable Fractional Integrals for h-Convex Functions

In this paper, we establish new Milne–Mercer-type inequalities via Atangana–Baleanu conformable fractional integral operators for differentiable functions whose derivatives in absolute value are h-convex. First, we derive a novel identity involving the Atangana–Baleanu conformable fractional integral operators. Then, by employing the properties of h-convex functions and fractional integral operators, several new inequalities of the Milne–Mercer type are obtained. The results presented in this paper extend and generalize various previously known inequalities, including classical Milne inequalities, Riemann–Liouville fractional integral inequalities, and conformable fractional integral inequalities. Moreover, several special cases are discussed to demonstrate the generality and applicability of the obtained results. The findings provide new refinements in the theory of fractional integral inequalities and contribute to the development of convex analysis within fractional frameworks.