This article investigates the performance of an unmanned aerial vehicle (UAV)-assisted wireless power transfer (WPT)-enabled communications for energy-constrained wireless devices. Herein, a UAV serves as a radio frequency (RF) energy harvesting (EH) transmitter for a pair of Internet-of-Things devices (IoDs). It also provides relay cooperation to IoDs using decode-and-forward (DF) operation. The composite fading channels associated with the UAV and IoDs are modeled by considering the probability of line-of-sight (LoS)/non-LoS (NLoS) and shadowing components, assuming log-normal distribution. Besides, the small-scale fading scenarios for LoS and NLoS communications are assumed to follow Nakagami-${m}$and Rayleigh distributions, respectively. In addition, considering relative mobility between the UAV and IoDs, we exploit the first-order autoregressive process to model the fading channels during the information transmission (IT) phase. For such a realistic system setup, we derive the expressions for the outage probability (OP) at the IoDs using Gauss-Hermite quadrature under different shadowing and fading channel combinations. The system throughput and energy efficiency are also quantified using the derived OP expressions. The analytical findings are verified through numerical and simulation results. Our results highlight the impact of various system/channel parameters on the system’s performance and provide significant insights into the system’s behavior.