<p>Fractional-order systems, known for their long memory properties, are well-suited for modeling and analyzing biological signals like EEG, offering advantages over traditional integer-order systems. This article proposes a method for extracting slow waves from EEG signals using a combination of fractional-order high pass and low pass filters. Unlike conventional integer-order FIR or IIR filters, which require significantly higher orders and thus lead to increased computational and storage demands, this approach provides a more efficient alternative. Additionally, fractional-order systems can be broken down into integers and fractions. The work uses a commensurate fractional order system that effectively represents the state space and meets the conditions of minimum phase and stability to distinguish slow wave activity in epileptic EEG waves. This approximation is obtained using the Hankel integration path and the residue theorem. EEG analysis for epileptic seizures is performed without any changes in the structure of the system.</p>