In digital signal processing applications and biomedical research one of the challenging areas of research is Electroencephalogram (EEG) signal processing. Electroencephalogram (EEG) is a neurophysiologic measurement that records the EEG signal from electrodes placed on the scalp to study the electrical activity of the brain. The EEG signal is combined with other biological signals called artefacts. Removing artefacts from EEG signals is a crucial task in the medical field. To improve the quality of the EEG signal and to reduce the noise, a Fractional Calculus Cat Swarm (FCCS) based enhanced adaptive filtering neural network model is introduced. The EEG was initially fed into an adaptive filter NARX network, whose weights are renowned by the FCCS algorithm. The cat swarm optimization (CSO) algorithm plays a vital role in producing a better optimal solution and fractional calculus is included to incorporate previous weights in the updated solution of weights. Finally, the performance of the proposed method is compared with existing methods in terms of SNR, MSE, and correlation coefficient.