Dynamic mobility management in fog computing has become vital for supporting seamless IoT operations as devices increasingly exhibit mobility. Traditional cloud-based solutions struggle with latency, bandwidth, and real-time processing, which fog computing addresses by extending computational resources to the network edge. This study introduces a dynamic mobility management service with a novel algorithm proposed for managing service continuity in fog computing microservices architecture supporting IoT applications named Dynamic Mobility-Aware Task Allocation and Handoff (DMATH). DMATH addresses this challenge through a proactive, multi-objective optimization architecture that integrates mobility prediction, latency-aware resource allocation, and seamless handoff management. The algorithm employs a mathematical model to forecast device trajectories, select optimal fog nodes based on a weighted scoring function, and redistribute tasks to avoid overload and service interruption. Compared to existing approaches such as MobFogSim, LATA, CAMM, and GRE. DMATH demonstrates superior performance in task completion time, latency compliance, handoff success rate, and scalability with corresponding rates of 90%, approximately 40 ms, and nearly 4335 handoff events. Key contributions include a decentralized mobility model based on microservices architecture with the ability to provide flexible services, resource utilization analysis under mobility scenarios, and latency-aware handover protocols. Results indicate significant improvements in latency, reliability, and scalability.