Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems
- This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar systems and for the Mittag-Leffler stability of an equilibrium point to fractional order nonlinear planar systems. To achieve these goals, our approach is as follows. Firstly, based on Cauchy’s argument principle in complex analysis, we obtain various explicit sufficient conditions for the asymptotic stability of linear systems whose coefficient matrices are constant. Secondly, by using Hankel type contours, we derive some important estimates of special functions arising from a variation of constants formula of solutions to inhomogeneous linear systems. Then, by proposing carefully chosen weighted norms combined with the Banach fixed point theorem for appropriate Banach spaces, we get the desired conclusions. Finally, numerical examples are provided to illustrate the effect of the main theoretical results.
Author: | Kai Diethelm, Ha Duc Thai, Hoang The Tuan |
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DOI: | https://doi.org/https://doi.org/10.1007/s13540-022-00065-9 |
ISSN: | 1314-2224 |
Parent Title (English): | Fractional Calculus and Applied Analysis |
Document Type: | Article |
Language: | English |
Date of first Publication: | 2022/08/04 |
Publishing Institution: | Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt |
Release Date: | 2023/02/22 |
Tag: | asymptotic behaviour of solutions; non-commensurate fractional order planar systems |
Volume: | 25 |
First Page: | 1324 |
Last Page: | 1360 |
Institutes and faculty: | Fakultäten / Fakultät Angewandte Sozialwissenschaften |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 515 Analysis |
Regensburger Klassifikation: | Mathematik |
Open access colour: | Hybrid |
Licence (German): | Creative Commons - CC BY - Namensnennung 4.0 International |