This paper’s main objective is to create a digital fractional order differentiator (DFOD) that is precise, wideband, and stable. First, the Honey Badger algorithm (HBA) has been used to build the first order s to z transform by minimizing the \(L_1\) -norm based error function. Performance comparison of designs based on real coded genetic algorithms (RCGA) and differential evolution (DE) and HBA-based first order transformations. Later, the indirect discretization of the new s to z transform using continuing fraction expansion (CFE) was used to develop the fourth and fifth orders for half and one-third fractional order differentiators. The RCGA and DE-based designs are contrasted with the relative magnitude error (RME) analysis of DFODs utilizing the HBA-based transform. The suggested approach performs better in terms of its magnitude response when compared to the current methods, demonstrating the superiority of the suggested HBA-based DFODs. The maximum absolute RME values of the fifth order for half and one-third of DFODs were obtained as \(-46.27\, dB\) and \(-49.12\, dB\) respectively.
