Skip to main content
Log in

Comments on “Stability analysis of Caputo fractional-order nonlinear systems revisited”

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This note points out that the proof for a widely and mostly used (uniform) asymptotic stability theorem for Caputo fractional-order systems, presented by the article “Stability analysis of Caputo fractional-order nonlinear systems revisited” published in Nonlinear Dynamics, is incorrect.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, New York (2010)

    Book  Google Scholar 

  2. Vainikko, G.: Which functions are fractionally differentiable? J. Anal. Appl. 35, 465–487 (2016)

    MathSciNet  MATH  Google Scholar 

  3. Delavari, H., Baleanu, D., Sadati, J.: Stability analysis of Caputo fractional-order nonlinear systems revisited. Nonlinear Dyn. 67, 2433–2439 (2012)

    Article  MathSciNet  Google Scholar 

  4. Bihari, I.: A generalization of a lemma of bellman and its application to uniqueness problems of differential equations. Acta Mathematica Academiae Scientiarum Hungaricae 7, 81–94 (1956)

    Article  MathSciNet  Google Scholar 

  5. Tuan, H.T., Trinh, H.: Stability of fractional-order nonlinear systems by Lyapunov direct method. IET Control Theory Appl. 12(17), 2417–2422 (2018)

    Article  MathSciNet  Google Scholar 

  6. Li, Y., Chen, Y.Q., Podlubny, I.: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45, 1965–1969 (2009)

    Article  MathSciNet  Google Scholar 

  7. Li, Y., Chen, Y.Q., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59(5), 1810–1821 (2010)

    Article  MathSciNet  Google Scholar 

  8. Naifar, O., Makhlouf, A.B., Hammami, M.A.: Comments on “Mittag-Leffler stability of fractional order nonlinear dynamic systems [Automatica 45(8) (2009) 1965–1969]. Automatica 75, 329 (2017)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cong Wu.

Ethics declarations

Conflicts of interest

The author declares that he has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, C. Comments on “Stability analysis of Caputo fractional-order nonlinear systems revisited”. Nonlinear Dyn 104, 551–555 (2021). https://doi.org/10.1007/s11071-021-06279-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06279-5

Keywords

Navigation