An improvement of the rational approximation of the fractional operatorsα

In this paper we propose an improvement of the rational approximation of continuous fractional order differentiators and integrators of types^α obtained using direct discretization approach of power series expansion-signal modeling technique by using a new second order s-to-z transform obtained by inversion and stabilizing the digital integrator designed from conventional Simpson integrator and fractional delay filter. The obtained new IIR type digital fractional order differentiators have much better frequency characteristic as compared to the Al-Alaoui operator based approximations. Furthermore, this paper compares the approximations obtained using PSE-truncation method and those obtained using PSE-modeling, the later best approximates^α.