The main objective of this paper is to design efficient one-half, one-third, and one-fourth non-integer order digital differentiators. Using the fractional bilinear transform (FBT) technique and a genetic optimization algorithm, the first step is to minimize the \(L_1\) -norm based fitness function to produce the integer order s to z transform. Later, the fractional order digital differentiators (FODDs) achieved by direct discretization approach using continued fraction expansion (CFE) of novel optimal transform. The mathematical models for the second, third, fourth, and fifth-order transfer functions of the fractional differentiators are developed. The frequency response of the proposed fractional digital differentiators acquire by using MATLAB simulation software. The efficacy of proposed FODDs was evaluated based on the maximum absolute magnitude error (AME), root mean square magnitude error (RMSME), and mean phase error (MPE) values. The performance of the proposed ones is compared with the available existing techniques and it is observed that the proposed method outperforms in terms of its magnitude and linear phase responses.
