Optimal Biquadratic Approximation of the Fractional-Order Laplacian Operator Yielding Improved Constant-Phase Behavior

This paper deals with the biquadratic approximation of the fractional-order Laplacian operator
$s^{\mathfrak{a}}$
, where,
$\alpha\in(0,1)$
. The coefficients of the proposed rational function are optimally determined using an efficient constrained evolutionary algorithm. The proposed design constraint helps to attain the theoretical phase value of
$\alpha\pi/2$
radians at the center frequency. Results showcase improved constant phase behavior for the proposed optimal approximants as compared to the models based on two different versions of the continued fraction expansion technique and the Sanathanan-Koerner curve-fitting method.