On the Theory of Multiplicative Conformable Fractional Integrals and Their Applications to Hermite-Hadamard and Maclaurin-Type Inequalities

This paper introduces multiplicative conformable fractional integrals within the setting of [Formula: see text]-calculus, a non-Newtonian framework naturally suited for positive functions with positive arguments. This new operator combines the flexibility of conformable fractional calculus with the multiplicative structure of [Formula: see text]-calculus, offering a promising tool for modeling scale-invariant and exponentialtype phenomena. We begin by defining the multiplicative conformable integrals. Subsequently, based on iterated multiplicative conformable integrals, we construct the multiplicative conformable fractional integrals and investigate their fundamental properties. Finally, as an application, we establish associated multiplicative Hermite-Hadamard and Maclaurin-type inequalities via [Formula: see text]-convexity.