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

Vietnam Journal of Mathematics volume 46, pages 665–680 (2018)Cite this article

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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Authors and Affiliations

  1. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam

    Nguyen D. Cong, Thai S. Doan & Hoang T. Tuan

Authors
  1. Nguyen D. Cong
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  2. Thai S. Doan
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  3. Hoang T. Tuan
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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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  • DOI: https://doi.org/10.1007/s10013-018-0272-4

Keywords

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

Mathematics Subject Classification (2010)

  • 34Dxx
  • 34A30
  • 26A33