Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Asymptotic behavior of solutions to some classes of multi-order fractional cooperative systems
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by La Van Thinh and Hoang The Tuan;
Proc. Amer. Math. Soc. 153 (2025), 1559-1574
DOI: https://doi.org/10.1090/proc/17119
Published electronically: February 18, 2025

Abstract:

This paper is devoted to the study of the asymptotic behavior of solutions to multi-order fractional cooperative systems. First, we demonstrate the boundedness of solutions to fractional-order systems under certain conditions imposed on the vector field. We then prove the global attractivity and the convergence rate of solutions to such systems (in the case when the orders of fractional derivatives are equal, the convergence rate of solutions is sharp and optimal). To our knowledge, these kinds of results are new contributions to the qualitative theory of multi-order fractional positive systems and they seem to have been unknown before in the literature. As a consequence of this result, we obtain the convergence of solutions toward a nontrivial equilibrium point in an ecosystem model (a particular class of fractional-order Kolmogorov systems). Finally, some numerical examples are also provided to illustrate the obtained theoretical results.
References
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Bibliographic Information
  • La Van Thinh
  • Affiliation: Academy of Finance, No. 58, Le Van Hien St., Duc Thang Wrd., Bac Tu Liem Dist., Hanoi, Viet Nam
  • MR Author ID: 1520688
  • ORCID: 0000-0002-7595-9836
  • Email: lavanthinh@hvtc.edu.vn
  • Hoang The Tuan
  • Affiliation: Department of Mathematics, Great Bay University, Dongguan, Guangdong 523000, People’s Republic of China; and Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Hanoi, Viet Nam
  • MR Author ID: 1016449
  • Email: tuanht@gbu.edu.vn
  • Received by editor(s): November 19, 2023
  • Received by editor(s) in revised form: July 11, 2024
  • Published electronically: February 18, 2025
  • Additional Notes: The second author was partly supported by the Guangdong Basic and Applied Basic Research Foundation (2023A1515140016).
  • Communicated by: Wenxian Shen
  • © Copyright 2025 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 153 (2025), 1559-1574
  • MSC (2020): Primary 34A08, 34K37, 45G05, 45M05, 45M20
  • DOI: https://doi.org/10.1090/proc/17119