In this paper, two second-order generating functions have been suggested to model a class of fractional-order system (FOS) in z domain using direct discretization method. The generating functions named as Goswami et al. operator (Method-I) and Mekhnache et al. operator (Method-II) are employed to obtain the approximated models of fractional-order differentiator (FOD) of one-fourth order and one-fifth order via continued fraction expansion (CFE). Further, these two methods have been used to model another two FOSs taken from the literature. Frequency responses of the approximated models show that Method-I has produced less root mean square error (RMSE) than Method-II and hence appears to be more effective to approximate the FOS.