Muhammad Aamir AliMichal Fe_kanChanon PromsakonThanin Sitthiwirattham2025-03-102025-03-102024Mathematica Slovaca139991810.1515/ms-2024-01052-s2.0-85217052140https://repository.dusit.ac.th//handle/123456789/4511The primary goal of this paper is to define Katugampola fractional integrals in multiplicative calculus. A novel method for generalizing the multiplicative fractional integrals is the Katugampola fractional integrals in multiplicative calculus. The multiplicative Hadamard fractional integrals are also novel findings of this research and may be derived from the special situations of Katugampola fractional integrals. These integrals generalize to multiplicative Riemann-Liouville fractional integrals and multiplicative Hadamard fractional integrals. Moreover, we use the Katugampola fractional integrals to prove certain new Hermite-Hadamard and trapezoidal-type inequalities for multiplicative convex functions. Additionally, it is demonstrated that several of the previously established inequalities are generalized from the newly derived inequalities. Finally, we give some computational analysis of the inequalities proved in this paper. © 2024 Mathematical Institute Slovak Academy of Sciences.convex functionsHermite-Hadamard inequalitymultiplicative calculusArticleScopus