<p>This paper presents a predictive methodology based on an uncertainty-corrected fractional generalized Pareto motion (fGPM) to address challenges in self-capacity regeneration and stochastic fluctuations in lithium-ion batteries. The approach uses probabilistic adjustments via Wasserstein distance and transitional Markov chain Monte Carlo methods to capture long-range dependencies and unique capacity regeneration behaviors. Our refined fGPM model achieves a root mean square error of 6.9426 and a mean absolute error of 5.8000, significantly outperforming advanced machine learning models like DCNN and TSO-LSTM, as well as stochastic process models such as fractional-order Lévy and Wiener process-based methods. Additionally, we introduce a value at risk-based maintenance strategy that integrates risk management with predictive insights. This strategy enables the development of dynamic, risk-adjusted maintenance plans tailored to varying operational conditions. The proposed method and maintenance strategy show superior performance and practical applicability in battery environments characterized by frequent capacity regeneration and stochastic fluctuations, enhancing equipment longevity and optimizing maintenance efficiency.</p>