Accurate and trustworthy prediction of lithium-ion battery aging remains challenging due to multi-mechanistic degradation, cell-to-cell variability, and distribution shift between laboratory calibration and deployment. Fractional-order models have been proposed to capture long-memory effects in electrochemical systems; however, it remains unclear when such memory is empirically identifiable and beneficial within the common prognostics abstraction of state-of-health (SOH) versus cycle index. This work develops a fully reproducible computational pipeline for mechanistic battery aging based on a Caputo fractional differential equation (FDE) and evaluates its cross-cell generalization on open NASA cycling data. Parameters are identified using bounded robust nonlinear least squares and validated under a strict transfer protocol: calibration on cells B0005/B0006 and evaluation on held-out cells B0007/B0018 without refitting. The fractional model is benchmarked against a classical ODE surrogate, an ECM-inspired resistance-proxy baseline, and one-step-ahead machine-learning predictors. Uncertainty quantification is performed via parameter bootstrap and subsequently calibrated using conformal correction to target nominal coverage under transfer. Results show that the fractional order tends to collapse toward the integer-order limit (α → 1) in this dataset, indicating limited evidence of additional long-memory at the SOH-versus-cycle level under the considered protocol, while robust identification remains essential for stability. Calibrated prediction intervals achieve near-nominal coverage on held-out cells, highlighting the importance of UQ calibration under cell-to-cell shift. The proposed scripts and environment specifications enable direct replication and facilitate future extensions to stress-aware fractional models and hybrid physics–ML approaches.
Guerra et al. (Thu,) studied this question.