Asymptotic Stability of Linear Fractional Systems with Constant Coefficients and Small Time-Dependent Perturbations

Abstract

Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable and then under the action of small (either linear or nonlinear) nonautonomous perturbations, the trivial solution of the perturbed system is also asymptotically stable.

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Acknowledgements

The authors are grateful to the referees for reading this paper and his/her comments and suggestions which helped to improve its content.

Funding

This research of the authors is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.03-2017.01. The authors are grateful to the referees for reading this paper and his/her comments and suggestions which helped to improve its content.

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Correspondence to Nguyen D. Cong.

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Cong, N.D., Doan, T.S. & Tuan, H.T. Asymptotic Stability of Linear Fractional Systems with Constant Coefficients and Small Time-Dependent Perturbations. Vietnam J. Math. 46, 665–680 (2018). https://doi.org/10.1007/s10013-018-0272-4

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Keywords

  • Fractional differential equations
  • Linear systems
  • Stability
  • Asymptotic stability

Mathematics Subject Classification (2010)

  • 34Dxx
  • 34A30
  • 26A33