The Internet of Things (IoT) has revolutionized the way we collect and process data, but it also poses significant energy challenges, especially in resource-constrained environments. Fog computing has emerged as a promising paradigm for addressing these challenges by moving data processing closer to IoT devices. This paper presents energy-optimized fog computing models tailored to IoT environments. Through innovative algorithms and resource management techniques, these models aim to minimize energy consumption while ensuring efficient data processing and communication. We explore the application of these models in real-world IoT scenarios, demonstrating their potential to prolong device lifespans, reduce energy costs, and enhance sustainability.