Abstract
In this paper, new discretized models of fractional order differentiator (FOD) (sr) and fractional order integrator (FOI) (s−r) based on first and higher order operators are proposed. Specifically in this work, one-third (s±⅓) and one-fourth (s±¼) order differentiator and integrator models based on first order Al-Alaoui [1] and Hsue operator [2], second order Schneider operator [3] and third order Al-Alaoui - Schneider-Kaneshige-Groutage (ALSKG) rule [4, 5] have been derived. The stability of the proposed models has been investigated and the unstable ones stabilized by the pole reflection method. Performance results using the proposed discrete-time formulations are found to converge to the analytical results of fractional order differentiator and integrator, in the continuous-time domain. MATLAB simulation results show that the responses of the fractional differentiators and integrators match with the results of the theoretical results of the continuous-time domain fractional differentiators and integrators.
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