This contribution presents a modeling technique for an aerial manipulator based on a quad-rotor vehicle provided with a robotic arm. Dual quaternions, which are a little explored but powerful mathematical tool, are proposed as an alternative to the classical Euler angles approach for the kinematic and dynamic modeling. A feedback control law based on dual quaternions is used to validate the proposed model, taking into account the external effects of the robotic limb. Numerical simulations and experiments validate the proposal, opening a path for future research.