We present existence and controllability results for mild solutions to the Atangana–Baleanu fractional evolution equations. We prove our results by applying bounded integral contractors and a sequencing technique. In contrast to the papers available in the literature, in order to establish our controllability results, we need not define the induced inverse of the controllability operator, and the pertinent nonlinear function need not necessarily satisfy a Lipschitz condition. In addition, we also establish trajectory controllability results. Finally, we discuss an application, which illustrates our results.