On Multiplicative Fractional Operators of Hadamard and Katugampola Types in <i>G</i> -Calculus and Related Hermite-Hadamard Inequalities

This paper explores the extension of classical fractional operators to the framework of [Formula: see text]-calculus, a non-Newtonian calculus in which differentiation and integration are defined via multiplicative analogues of their classical counterparts. We begin by recalling key concepts from both fractional calculus and [Formula: see text]-calculus. Next, we revisit the recently introduced multiplicative Riemann-Liouville fractional operators and extend the multiplicative Riemann-Liouville fractional derivative to arbitrary order [Formula: see text]. Building on this foundation, we introduce multiplicative versions of the Hadamard and Katugampola fractional integrals and derivatives. Finally, we establish Hermite-Hadamard inequalities for both newly defined integrals.