A fast frequency domain approximation method for variable order fractional calculus operator based on polynomial fitting

Fractional calculus and its application has been widely researched, and in most case the order is considered as a constant value. In many application fields the order is variable, and the fast implementation of variable order fractional calculus is important. In this paper a fast frequency domain approximation method for variable order fractional calculus operator is presented based on polynomial fitting. Firstly, the approximated integer order transfer functions for fractional calculus operator at several discrete order with equal interval are obtained by using the oustaloup method. Secondly, the coefficients from the same position in the approximated transfer functions corresponding to different order are taken out to construct coefficients matrix, then the column vectors of the coefficient matrix are used to make the polynomial fitting. Finally, for variable order, the approximated transfer functions in frequency domain can be achieved directly and quickly through the fitting function. The simulation results show the effectiveness of the proposed method.