In this paper, we introduce and study conformal algebras with brackets (CAWB), which generalize algebras with brackets to the conformal setting. After establishing their definition and basic properties, we provide an equivalent characterization of quadratic CAWB. We construct dendriform-CAWB structures via \(\mathcal {O}\) -operators. These results extend the operator approach of algebras with brackets to the conformal framework, revealing new structural connections with conformal algebra theory and related algebraic systems.
