In this paper, a new two-steps design strategy is introduced for the optimal rational approximation of the fractional-order Butterworth filter. At first, the weighting factors of the summation between the n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -order and the (n + 1) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -order Butterworth filters are optimally determined. Subsequently, this model is employed as an initial point for another optimization routine, which minimizes the magnitude-frequency error relative to the (n+α) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -order, where α ∈ (0, 1), Butterworth filter. The proposed approximant demonstrates improved performance about the magnitude mean squared error compared to the state-of-the-art design for six decades of bandwidth, but the introduced approach does not require a fractional-order transfer function model and the approximant of the s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> operator. The proposed strategy also avoids the use of the cascading technique to yield higher-order fractional-order Butterworth filter models. The performance of the proposed 1.5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -order Butterworth filter in follow-the-leader feedback topology is verified through SPICE simulations and its hardware implementation based on Analog Devices AD844AN-type current feedback operational amplifier.