The electric vehicle has become an important development direction of the automobile industry, and the lithium-ion power battery is the main energy source of electric vehicles. The accuracy of state of charge (SOC) estimation directly affects the performance of the vehicle. In this paper, the first order fractional equivalent circuit model of a lithium iron phosphate battery was established. Battery capacity tests with different charging and discharging rates and open circuit voltage tests were carried out under different ambient temperatures. The conversion coefficient of charging and discharging capacity and the simplified open circuit voltage model considering the hysteresis characteristics of the battery were proposed. The parameters of the first order fractional equivalent circuit model were identified by using a particle swarm optimization algorithm with dynamic inertia weight. Finally, the recursive formula of a fractional extended Kalman filter was derived, and the battery SOC was estimated under continuous Dynamic Stress Test (DST) conditions. The results show that the estimation method has high accuracy and strong robustness.