Design of Linear Analog Systems with Dynamics Represented by Atangana-Baleanu Fractional-Order Derivatives

This work presents the design of analog systems for Fractional-Order (FO) systems governed by the Atangana-Baleanu (AB) fractional derivative. A systematic design methodology is proposed for the development of analog circuits for FO systems based on Foster and Cauer network synthesis techniques, where the dynamics of systems are approximated using the Oustaloup recursive approximation. This approach enables analog realization of FO operators across a specified frequency band. The proposed analog system is designed and implemented using the LTspice simulation environment, which provides circuit-level analysis and includes advanced CMOS modeling. All circuit components are realized using a standard 180-nm CMOS technology process to ensure ease of implementation. The choice of 180-nm CMOS technology offers a balanced trade-off between device performance and design complexity, making it well-suited for analog and mixed-signal circuit realization. Time-domain and frequency-domain validations demonstrate that the designed analog systems faithfully capture the dynamics of the corresponding FO models. The time-domain performance indices of the designed systems, including rise time, settling time, peak overshoot, and the mean square error, are compared to the theoretical FO model responses.