The reduced availability of fossil fuels and the search for sustainable and possibly ecological energy resources has given a strong acceleration to the development of electric and hybrid electric vehicles. As a consequence, the demand for automotive batteries has increased and in particular of Lithium-ion batteries (LIBs). When using LIBs, an accurate estimation of the State-of-Charge (SOC) is fundamental to enlarge the usable energy capacity and to make the battery operate within the appropriate voltage and temperature limits. Moreover, a deeper insight into the diffusion processes in electrochemistry is beneficial for the development of rechargeable batteries. In this context, recently, fractional differential models have been proposed, to improve the existing ones based on integer order differential equations. Nevertheless, the analytical solutions of fractional differential problems are merely available only in very simple cases, therefore a numerical approach is necessary. In most situations, only a naïve discretization of the fractional derivative has been proposed. In this talk, we propose some advanced numerical methods for fractional differential equations, namely a class of spline collocation methods, which have high order of convergence and good stability properties. Nonstandard discretization schemes which preserve the positivity of the solution will also be considered.