This article investigates the commutators generated by BMO functions and the fractional integral operator \(I_{\alpha }\) in Orlicz-Morrey spaces. We establish a novel boundedness result for the commutator under a weaker condition on Young function than in previous work (Theorem 1.4 in Iida (Math. Ine. and Appl., 3, 26, 655-683, 2023)). For example, our condition allows the Young function \(\Psi \) to satisfy the \(\triangle _2\) -condition, without necessarily satisfying the \(\triangledown '\) -condition. We also provide a concrete example of Young functions satisfying our condition. Furthermore, we prove a new Olsen-type inequality for the commutator (Theorem 2.1), which extends the applicability of such inequalities to a wider class of operators, including, for example, the fractional integral operator and its commutators with BMO-functions.
