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Recently, unmanned aerial vehicle (UAV) acts as the aerial mobile edge computing (MEC) node to help the battery-limited Internet of Things (IoT) devices relieve burdens from computation and data collection, and prolong the lifetime of operating. However, IoT devices can ONLY ask UAV for either computing or caching help, and collaborative offloading services of UAV are rarely mentioned in the literature. Moreover, IoT device has multiple mutually independent tasks, which make collaborative offloading policy design even more challenging. Therefore, we investigate a UAV-enabled MEC networks with the consideration of multiple tasks either for computing or caching. Taking the quality of experience (QoE) requirement of time-sensitive tasks into consideration, we aim to minimize the total energy consumption of IoT devices by jointly optimizing trajectory, communication and computing resource allocation at UAV, and task offloading decision at IoT devices. Since this problem has highly non-convex objective function and constraints, we first decompose the original problem into three subproblems named as trajectory optimization ($$\mathbf {P}_{\mathbf {T}}$$ P T ), resource allocation at UAV ($$\mathbf {P}_{\mathbf {R}}$$ P R ) and offloading decisions at IoT devices ($$\mathbf {P}_{\mathbf {O}}$$ P O ) and then propose an iterative algorithm based on block coordinate descent method to cope with them in a sequence. Numerical results demonstrate that collaborative offloading can effectively reduce IoT devices’ energy consumption while meeting different kinds of offloading services, and satisfy the QoE requirement of time-sensitive tasks at IoT devices.