In this paper, we initiate the study of impulsive controls in the context of impulsive fractional order differential equations with Caputo derivative of order $\alpha\in (0,1)$ and present several results highlighting their significance. We address the problem of determining the existence and uniqueness of the considered fractional systems and provided the necessary and sufficient conditions. We provide a solution representation in the form of $\alpha$ families, using semigroup and impulsive operators, based on the fundamental assumption that the operator \(A\), which governs the state, is the infinitesimal generator of a strongly continuous semigroup. Finally, we include an example to illustrate and verify all the obtained results.