Cloud computing is the pradigim where service providers carry-on computational tasks for their customers. Multi-access Edge Computing (MEC) is a recent form of service where the computational tasks are carried in a distributed manner at the edge of the network to be as close to customer as possible. This new pradigim have the advantage of lowering the latency, making the pradigim suitable for real-time applications. One promising way to deploy MEC is to mount the servers over a UAV which can be moved dynamically to become closer to users. In this paper, we address the challenges associated with UAV-mounted servers like energy consumption and path routing. We propose a UAV control mechanism based on continuous-time Markov Decision Process (CT-MDP). We demonstrated the advantage of the proposed mechanism in terms of task-satisfaction rate and policy computational time.