For electric vehicle (EV) or hybrid EV (HEV) development and integration of renewables in electrical networks, battery monitoring systems have to be more and more precise to take into account the state-of-charge and the dynamic behavior of the battery. Some non-integer order models of electrochemical batteries have been proposed in literacy with a good accuracy and a low number of parameters in the frequential domain. Nevertheless, time simulation of such models required to approximate this non-integer order system by an equivalent high integer order model. An adapted algorithm is then proposed in this article to simulate the non-integer order model without any approximation, thanks to the construction of a 3-order generalized state-space system. This algorithm is applied and validated on a 2.3 A.h Li-ion battery.