Geodesic
Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization
Fractional calculus and applied analysis, Tome 11 (2008) no. 2, pp. 143-151.

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In this paper, design of fractional order digital differentiators and integrators using indirect discretization is presented. The proposed approach is based on using continued fraction expansion to find the rational approximation of the fractional order operator, s^α. The rational approximation thus obtained is discretized by using s to z transforms. The proposed approach is tested for differentiators and integrators of orders 1/4 and 1/2. The results obtained compare favorably with the ideal characteristics.
Keywords: Fractional Order Integrator, Fractional Order Differentiator, Continued Fraction Expansion, Al-Alaoui Transform 
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     author = {Krishna, B. and Reddy, K.},
     title = {Design of {Fractional} {Order} {Digital} {Differentiators} and {Integrators} {Using} {Indirect} {Discretization}},
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Krishna, B.; Reddy, K. Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization. Fractional calculus and applied analysis, Tome 11 (2008) no. 2, pp. 143-151. http://geodesic.mathdoc.fr/item/FCAA_2008_11_2_a1/