In this paper, an extension of Darbo's fixed point theorem via the concept of operators A(f ; .) and θ-ω-contractions in a Banach space has been presented. We illustrate that some conditions of control functions ϑ and ω can be omitted where they applied previously in [ Mohammadi et al., Mathematics, 2020, 8(4), 492]. As an application, we study the existence of solutions for a system of fractional integral equations. Finally, to support the effectiveness of our results, we present an example