Efficient Design of DFODs Using GBMO

Design of an IIR type digital fractional-order differentiator (DFOD) by adopting competent metaheuristic Gases Brownian Motion Optimisation (GBMO) algorithm is proposed in this article. The GBMO algorithm simulates the turbulent rotational and Brownian motions of the gas molecules $(G_{m})$ to solve the optimisation problem. The position of the gas molecule, which is associated with the lowest cost value is selected as the close to universal optimal result for the optimisation problem. The optimal designs of second and fifth-order DFODs have been carried out, and the mean absolute relative magnitude error is used as the performance measure to estimate the quality of the designed DFODs. The experimental results demonstrate the efficacy of the GBMO to solve DFOD type complex design problem and the resulted solutions sensibly surpass the state-of-the-art reported DFOD design approaches.