The paper presents an adaptive control for an aerial vehicle equipped with a manipulator, the latter is assumed to be already driven by a joint-based controller. The proposed control generates the vehicle thrusts by properly taking into account the physical interaction with the arm. Being adaptive, it estimates and then compensates the dynamics of the whole system. Moreover, the proposed approach is based on the Newton- Euler formulation, i.e., it is recursive. A stability analysis is provided to analytically support the developed controller. A reduced version is proposed to greatly simplify the controller by taking into account only the gravitational terms. Numerical simulations confirm the controller performance as compared with the effort and error of a benchmark controller.