The rapid advancement in wireless communication technology enables the drones to offer flexible and resilient offloading services to the mobile users in the presence of limited terrestrial infrastructure. However, the interaction between users and drones being in an open environment has raised critical security and privacy concerns. In this paper, we propose integrating the proof-of-work (PoW)-based consensus blockchain technology into the network to tackle these challenges. Specially, the drones are tasked with economically incentivizing the edge computing nodes as the miners to compete for the block generation privilege by solving cryptographic puzzles. We formulate a two-stage Stackelberg differential game to allocate edge computing resources between the drones and miners, leveraging the average reputation of miners to solve for dynamic task pricing. Additionally, the drones and miners take on the roles of leaders and followers in this game, respectively. By solving the openloop Stackelberg equilibrium, we derive the evolving trend of the optimal strategies for the system in the dynamic pricing environment. Furthermore, the numerical results substantiate the effectiveness and feasibility of this proposed scheme.