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In this paper, we study the resource allocation and trajectory design for secure unmanned aerial vehicle (UAV)-enabled communication systems, where multiple multi-purpose UAV base stations are dispatched to provide secure communications to multiple legitimate ground users (GUs) in the existence of multiple eavesdroppers (Eves). Specifically, by leveraging orthogonal frequency division multiple access (OFDMA), active UAV base stations can communicate to their desired ground users via the assigned subcarriers while idle UAV base stations can serve as jammer simultaneously for communication security provisioning. To achieve fairness in secure communication, we maximize the average minimum secrecy rate per user by jointly optimizing the communication/jamming subcarrier allocation policy and the trajectory of UAVs, while taking into account the constraints on the minimum safety distance among multiple UAVs, the maximum cruising speed, the initial/final locations, and the existence of cylindrical no-fly zones (NFZs). The design is formulated as a mixed integer non-convex optimization problem which is generally intractable. Subsequently, a computationally-efficient iterative algorithm is proposed to obtain a suboptimal solution. Simulation results illustrate that the performance of the proposed iterative algorithm can significantly improve the average minimum secrecy rate compared to various baseline schemes.