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

Abstract

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.

Keywords

• Fractional-order circuits and systems
• nonlinear circuits and systems
• fractional-order electrical elements
• stability analysis
• dynamical behavior analysis