Asymptotic Solutions and Circuit Implementations of a Rayleigh Oscillator Including Cubic Fractional Damping Terms

作者：Xiao, Min^*; Jiang, Guoping; Cao, Jinde

来源：Circuits, Systems, and Signal Processing, 2016, 35(6): 2041-2053.

DOI：10.1007/s00034-016-0268-9

• Caputo derivative
• Fractional-order Rayleigh oscillator
• Asymptotic solution
• Two-scale expansion method
• Circuit implementation

This paper proposes a fractional-order Rayleigh oscillator model, which involves a cubic damping term described by fractional derivatives. The presence of such fractional damping term makes the analysis more difficult. A two-scale expansion method is employed for asymptotic solutions of the fractional-order Rayleigh oscillator. Then, an example is provided to compare the asymptotic solutions with the numerical solutions. The numerical results demonstrate the validity and applicability of the proposed method to solve fractional differential equations with high order fractional terms. Furthermore, an electronic circuit is designed to realize the fractional-order Rayleigh oscillator.

• 出版日期2016-6
• 单位南京邮电大学; 东南大学