Numerical properties of discrete approximations of an elementary fractional order transfer function

The paper deals with the analysis of basic numerical properties of discrete approximations of the elementary fractional order, inertial transfer function. The considered transfer function is approximated with the use of two most typical approaches. The first one uses Continuous Fraction Expan-sion (CFE) approximation, the next one employes the Fractional Order Backward Difference (FOBD) approximation, based on the Grunwald-Letnikov (GL) definition of fractional operator. Elementary properties of both approximants: accuracy and duration of calculations are numerically analysed using PC and MATLAB. Publications in this field are not known to the author.Results of numerical tests point that at the considered software-hardware platform the FOBD approximation assures better accuracy than CFE ap-proximation with practically the same duration of computation. Next, the speed of computing is determined by the form of source code. Additionally, the computing of step response with the use of both tested approximations is much faster than the use of analytical solution employing the MATLAB implementation of Mittag-Leffler function.