Volume 29, 2023
|Number of page(s)||35|
|Published online||11 August 2023|
Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, Viet Nam
2 Department of Mathematics, Great Bay University, Dongguan, Guangdong 523000, PR China
3 Academy of Finance, No. 58, Le Van Hien St., Duc Thang Wrd., Bac Tu Liem Dist., Hanoi, Viet Nam
* Corresponding author: firstname.lastname@example.org
Accepted: 21 July 2023
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear systems with time-varying delays. Next, we obtain necessary and sufficient criteria which characterize the positivity of mixed-order delay linear coupled systems. Our main contributions are in Section 5. More precisely, by using a smoothness property of solutions to fractional differential equations and developing a new appropriated comparison principle for solutions to mixed-order delay positive systems, we prove the attractivity of mixed-order non-homogeneous linear positive coupled systems under the impact of bounded or unbounded delays. We also establish a necessary and sufficient condition to| ensure the stability of homogeneous systems. As a consequence of these results, we show the smallest asymptotic bound of solutions to mixed-order delay positive non-homogeneous linear coupled systems where disturbances are continuous and bounded. Finally, we provide numerical simulations to illustrate the proposed theoretical results.
Mathematics Subject Classification: 34A08 / 34K37 / 45A05 / 45M05 / 45M10 / 45M20
Key words: Fractional differential equations / mixed-order systems with bounded or unbounded delays / positive coupled systems / existence and uniqueness / asymptotic behavior of solutions / smallest asymptotic bounded of solutions
© The authors. Published by EDP Sciences, SMAI 2023
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