The ambulance routing problem plays a critical role in emergency medical services, where timely ambulance response can significantly impact patient outcomes. However, urban traffic congestion and dynamic routing conditions cause challenges to existing optimization approaches. This study proposes CaputoGA, a novel hybrid metaheuristic that integrates the Caputo fractional derivative into the genetic algorithm framework. By introducing a memory-aware penalty term and adaptive mutation rate based on this fractional derivative, CaputoGA enhances convergence behavior and routing stability. The algorithm is further enhanced with a hybrid local search mechanism combining 2-opt and swap heuristics to refine best routes. Experimental evaluations on benchmark datasets adapted from the vehicle routing problem demonstrate that CaputoGA outperforms standard GA and two state-of-the-art hybrid algorithms, such as K-means simulated annealing tabu search and priority-based adaptive particle swarm optimization, in both route cost and robustness. Experimental results show that CaputoGA substantially reduces the percentage difference relative to the known cost and can achieve the lowest percentage difference at 3.98%. CaputoGA also requires shorter execution time in completing best routes calculation compared to GA. These results validate the efficacy of implementing memory-driven dynamics into evolutionary search. This work highlights the potential of fractional calculus in optimizing complex routing problems and provides a foundation for future extensions into other metaheuristic approaches.