Milne‐Type Inequalities in the Context of Conformable Fractional Multiplicative Integrals

This paper examines Milne inequalities in the setting of conformal fractional multiplicative integrals, which represent a modern extension of traditional fractional calculus. Drawing on advances in multiplicative analysis and non‐Newtonian calculus, we establish a new integral identity that forms the basis for deriving Milne‐type inequalities for multiplicatively convex functions with bounded ∗ derivatives. Using this framework, we derive new error estimates and integral bounds under relatively mild conditions. To demonstrate the applicability of our results, we present a numerical example with graphical representations. We also extend the analysis to functions subject to certain derivative constraints and discuss an application to specialized tools. The paper concludes by highlighting key contributions and suggesting possible directions for future research in multiplicative fractional calculus.