In this paper, a Szasz-Favard-Mirakyan operator is exploited for chaos synchronization of a master-slave system. The universal approximation feature asset lets in Szasz-Favard-Mirakyan operators for approximating uncertainties, including un-modeled dynamics and disturbances. The above subject is considered in detail in this investigation. It is confirmed that the synchronization/approximation errors are uniformly bounded and stable if the Szasz-Favard-Mirakyan operators are applied as the regressors. Additionally, it has been presumed that the synchronization’s error rate is not available, and an observer will be designed for its estimation. The Duffing–Holmes oscillator is examined as the computer-generated chaotic framework with the target of examining the functioning of the recommended synchronization observer-based controller. The outcomes are compared with an effective approximation-based control strategy. Unlike Chebyshev Neural Network approximators in which the system’s inputs states are needed to define the regressor vector and approximate uncertainties, the suggested Szasz-Favard-Mirakyan operators–based strategy is independent of the system states for constructing the regressor vector.
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