Lithium ion batteries have attracted wide attention due to their high energy density, long cycle life, and environmental friendliness and are widely used in electrical vehicles. An accurate and reliable battery model is needed in battery management systems (BMS) to monitor battery operating conditions, including state of charge (SOC), state of health (SOH), etc. This paper presents a state-space model with non-integer order derivatives for electrochemical batteries with a constant phase element (CPE) in order to accurately describe battery dynamics. The proposed model is a combination of electrochemical impedance spectroscopy and the 1-RC model. The Oustaloup recursive approximation was selected for model parametric identification and potential implementation. A particle-swarm optimization (PSO) algorithm was used to identify three model parameters by using time-domain test data. The model accuracy and robustness were validated by using datasets from different driving cycles, aging levels and cells of the same chemistry. The proposed FOM showed good accuracy and robustness. It is suitable for research on battery reliability, including issues like SOC estimation, SOH prediction, and charging control.