On the nonexistence of non-constant exact periodic solutions in a class of the Caputo fractional-order dynamical systems
Release Time:2025-04-30
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- Date:
- 2025-04-30
- Title of Paper:
- On the nonexistence of non-constant exact periodic solutions in a class of the Caputo fractional-order dynamical systems
- Journal:
- NONLINEAR DYNAMICS
- Summary:
- Using Fourier analysis as tool, we prove that the Caputo fractional-order derivative of the nonconstant periodic function cannot be periodic, and thus we confirm the nonexistence of the non-constant exact periodic solutions in a class of the Caputo fractionalorder initial-valued dynamical systems (including the autonomous case) from a different viewpoint. We also demonstrate with theoretical discussion and numerical examples that the non-constant long-time periodic solution might exist in the Caputo fractional-order systems. The investigation clarifies the difference and similarity of the periodic solutions between the Caputo fractional-order dynamical systems and the integerorder dynamical systems in a systematic way.
- Co-author:
- Kang Yan-Mei, Xie Yong, Lu Jin-Cheng, Jiang Jun
- Volume:
- 82(3)
- Page Number:
- 1259-126
- Translation or Not:
- No
- Date of Publication:
- 2015-10-07