Discretization of Fractional Order Operator in Delta Domain

The fractional order operator is the backbone of system (FOS). (FOO) generally represented as s^(±μ) (0<μ<1). Discrete time FOS can be obtained through discretization operator. FOO general form either differentiator (FOD) or integrator (FOI) depending upon values μ. Out two methods, direct outperforms method indirect discretization. mapping between continuous and discrete domain done with development generating function. Continuous fraction expansion (CFE) used expand function for rational approximation FOO. There an inherent problem associated in z-domain particularly at very fast sampling rate. In other hand, using delta parameterization provides results hand to when systems are sampled rate circumventing shift this work, a new proposed discretize Gauss-Legendre 3-point quadrature rule expanded CFE domain. benchmark considered work simulation purpose comparison made prove efficacy MATLAB.