In this paper, a new resource allocation framework for unmanned aerial vehicle (UAV) assisted multicast wireless networks is proposed in which the network users according to their request are divided into several multicast groups. Power domain non-orthogonal multiple access is adopted as the transmission technology using which the dedicated signals of multicast groups are superimposed and transmitted simultaneously as the UAV passes over the communication area for fixed and mobile users. The proposed scenarios are discussed from two perspectives, offline and online modes. In offline mode, the problem is implemented for fixed and mobile users whose locations are predictable (the location of users, over the communication time, is known at the beginning of the communication time) and in online mode for mobile users whose locations are unpredictable (the location of users, over the communication time, is unknown at the beginning of the communication time). Also, a scenario is proposed in which the online mode the number of mobile users can grow in each time slot. The problem of joint power allocation and UAV trajectory design as an optimisation problem that is non-linear and non-convex for two proposed scenarios is formulated. To solve the problem, an alternate search method, successive convex approximation, and geometric programming are adopted. Using simulation results, the performance of the proposed scheme is evaluated for different values of the network parameters.