Comparison of Different Implementation Methods of Fractional-Order Derivative/Integral

Implementing a fractional-order operator requires many resources to acquire an accurate response compared to the theoretical response. In this paper, three implementation methods of digital fractional-order operators are exploited. The three implementation methods are based on FIR, IIR, and lattice wave digital filters. The three methods are implemented using different optimization algorithms to optimize the choice of the coefficients of the three filters. This optimization is done to approximate the frequency response of an ideal fractional operator. This comparison aims to determine each implementation method's accuracy and resource usage level to decide which method is better for different systems.