Urban Air Mobility (UAM) poses unprecedented traffic coordination challenges, especially with increasing UAV densities in dense urban corridors. This paper introduces a mathematical model using a control algorithm to optimize an Edge AI-driven decentralized swarm architecture for intelligent conflict resolution, enabling real-time decision-making with low latency. Using lightweight neural networks, the system leverages edge nodes to perform distributed conflict detection and resolution. A simulation platform was developed to evaluate the scheme under various UAV densities. Results indicate that the conflict resolution time is dramatically minimized up to 3.8 times faster, and accuracy is enhanced compared to traditional centralized control models. The proposed architecture is highly promising for scalable, efficient, and safe aerial traffic management in future UAM systems.