Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

• Published in: IEEE open journal of circuits and systems Vol. 1; pp. 220 - 232
• Main Authors: Tavazoei, Mohammad Saleh, Tavakoli-Kakhki, Mahsan, Bizzarri, Federico
• Format: Journal Article
• Language: English
• Published: New York IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Capacitors; Circuit design; Circuits; Design analysis; Differential equations; Dynamic models; dynamical behavior analysis; Fractional-order circuits and systems; fractional-order electrical elements; Inductors; Integrated circuit modeling; Memristors; nonlinear circuits and systems; Nonlinear dynamics; Operators (mathematics); Stability analysis; System effectiveness
• ISSN: 2644-1225; 2644-1225
• DOI: 10.1109/OJCAS.2020.3029254

In recent years, fractional-order differential operators, and the dynamic models constructed based on these generalized operators have been widely considered in design and practical implementation of electrical circuits and systems. Simultaneously, facing with fractional-order dynamics and the nonlinear ones in electrical circuits and systems enforces us to use more advanced tools (in comparison to those commonly used in design and analysis of linear fractional-order/nonlinear integer-order circuits and systems) for their analysis, design, and implementation. Discussing on such a motivation, this tutorial paper aims to provide an overview on the recent achievements in proposing effective tools for analysis and design of nonlinear fractional-order circuits and systems. Moreover, some open problems, which can specify future directions for continuing research works on the aforementioned subject, are discussed.