Fractional Order Federated Learning for Battery Electric Vehicle Energy Consumption Modeling

Federated learning on connected electric vehicles (BEVs) faces severe instability due to intermittent connectivity, time-varying client participation, and pronounced client-to-client variation induced by diverse operating conditions. Conventional FedAvg and many advanced methods can suffer from excessive drift and degraded convergence under these realistic constraints. This work introduces Fractional-Order Roughness-Informed Federated Averaging (FO-RI-FedAvg), a lightweight and modular extension of FedAvg that improves stability through two complementary client-side mechanisms: (i) adaptive roughness-informed proximal regularization, which dynamically tunes the pull toward the global model based on local loss-landscape roughness, and (ii) non-integer-order local optimization, which incorporates short-term memory to smooth conflicting update directions. The approach preserves standard FedAvg server aggregation, adds only element-wise operations with amortizable overhead, and allows independent toggling of each component. Experiments on two real-world BEV energy prediction datasets, VED and its extended version eVED, show that FO-RI-FedAvg achieves improved accuracy and more stable convergence compared to strong federated baselines, particularly under reduced client participation.