In this article, a fractional-order model (FOM)-based online state of charge (SOC) and state of power (SOP) estimation method is proposed for lithium-ion batteries in electric vehicles. First, the model parameters of a second-order FOM are globally optimized under the dynamic stress test profile, where two resistor-constant phase element networks are recognized to represent battery internal dynamics at different timescales. Second, to enhance the model performance in SOC and SOP estimation, a partial-adaptive FOM (PA-FOM) is realized by fixing the parameters of the first resistor-constant phase element network with slow dynamics while allowing the online adaption of the second resistor-constant phase element network with fast dynamics. Based on the PA-FOM, online SOC estimation is implemented using an adaptive extended Kalman filter algorithm while an unscented Kalman filter-based iterative approaching algorithm is devised to estimate SOP. The proposed method is validated under different EV driving profiles. The experimental results show that the PA-FOM has an outstanding performance in interpreting battery dynamics at different timescales and the proposed SOC and SOP estimation method is highly accurate and efficient.