In recent years, flying robots have gained popularity in a new application known as aerial robotic manipulation. This technology performs operations in dangerous and inaccessible environments, significantly reducing costs. However, combining a flying robot with a robotic arm increases system nonlinearity and coupling, leading to challenging control and path-tracking scenarios. There are two main approaches to robotic manipulation control: centralized and decentralized. This paper focuses on the decentralized approach, where the forces and torques from the robotic arm are treated as external disturbances acting on the flying robot. A novel adaptive robust Terminal sliding mode controller is employed to implement this decentralized control. The adaptive component estimates the limits of uncertainties and disturbances, ensuring finite-time convergence. Additionally, a backstepping sliding mode controller with a Lyapunov stability guarantee is developed for the flying robot. Finally, a simulation is presented for an unmanned aerial manipulator equipped with a two-degree-of-freedom active robotic arm. The simulation considers mass uncertainties during an oil rig inspection mission. The results demonstrate that the proposed controllers achieve optimal performance, enabling fast and accurate path tracking within a limited time.