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Abstract: fractional calculus is considered a useful tool for gaining deeper insights into systems with memory effects or history. Fractional-order modeling of nonlinear systems may increase the stiffness and complexity of the system, but also provides better insights. This study introduces a swarm intelligence-based parameter estimation of the fractional Hammerstein autoregressive exogenous noise (fractional-HARX) model. The Grünwald–Letnikov finite difference formula is used to develop the fractional-HARX model from the standard HARX model. This study presents the design of a swarm intelligence-based electric eel foraging optimization algorithm (EEFOA) for parameter estimation of the fractional-HARX model under multiple noise scenarios for second- and third-order polynomial type nonlinearity. The key-term separation principle is also incorporated in the system model to reduce the occurrence of redundant parameters due to cross-product terms in the information vector. The designed methodology is examined, and the superiority of EEFOA is endorsed in terms of convergence, robustness, stiff parameter estimation, and deviation from the mean point in comparison with state-of-the-art optimization heuristics such as the whale optimization algorithm, the African vulture optimization algorithm, Harris hawk’s optimizer, and the reptile search algorithm. The statistical significance of the EEFOA for the estimation of fractional-HARX models is also established using statistical indices of best, mean, and worst fitness values along with standard deviation for multiple noise scenarios.

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