Abstarct: In this thesis, in order to estimate the state of charge of lead-acid batteries that are studied here, the fractional order Kalman filter method is used, which is among the most recent and accurate models for estimating the state of charge of rechargeable batteries. In order to solve this problem and make a suitable and acceptable estimate, at first, by examining the common methods in determining the battery circuit model used to estimate the parameters of the battery model, the best model is extracted, and then the parameters of the selected model for the battery are extracted using existing algorithms. In the next step, using the information of the sample battery and the extracted parameters of the circuit model, the necessary equations are written in the state space for this sample circuit model, which is of the second-order RC type, then the obtained equations are analyzed in the discretized space, and the unknown quantities of the circuit are determined. and at the end, by examining and analyzing different methods of estimating the state of charge of the battery in the field of fractional order, the method of estimating the state of charge of the developed Kalman filter of fractional order, along with estimation and updating, the state of charge of the battery in question is estimated with great accuracy. This method is simulated by MATLAB software, which compares with the usual methods, the optimal amount of estimation is confirmed. Also, this thesis shows that the estimate obtained by the fractional order extended Kalman filter method has a lower estimation error and higher accuracy compared to the usual extended Kalman filter.