This paper investigates a novel joint content caching and energy harvesting scheme to enhance unmanned aerial vehicle (UAV) communications in Internet of Things non-orthogonal multiple access (NOMA) network, where a UAV is acted as an aerial relay to serve users on demand. In particular, a neoteric gravitational search-based multi-constraint optimization algorithm is designed to maximize the throughput of the served users by jointly optimizing power allocation, energy harvesting, and time scheduling schemes. The algorithm engages two main characteristics: 1) classification of multiple constraints, which is for reducing the complexity of the problem solving process due to multiple iterations, and 2) design of force sets, which aims to enhance the global search for the optimal solution at the feasible region boundary. Finally, simulations are provided to show the effective convergence and superiority of the proposed algorithm.