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Stability for coupled systems on networks with Caputo-Hadamard fractional derivative | ||
| Journal of Mathematical Modeling | ||
| دوره 9، شماره 1، فروردین 2021، صفحه 107-118 اصل مقاله (281.63 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2020.17303.1500 | ||
| نویسندگان | ||
| Hadjer Belbali1؛ Maamar Benbachir* 2 | ||
| 1Laboratoire de Mathematiques et Sciences appliquees, University of Ghardaia, Algeriaa | ||
| 2Faculty of Sciences, Saad Dahlab University, Blida, Algeria | ||
| چکیده | ||
| This paper discusses stability and uniform asymptotic stability of the trivial solution of the following coupled systems of fractional differential equations on networks \begin{equation*} \left\{ \begin{array}{l l l} ^{cH}D^{\alpha} x_{i}=f_{i}(t,x_{i})+\sum\limits_{j=1}^{n}g_{ij}(t,x_{i},x_{j}),&t> t_{0}, \\ x_{i}(t_{0})=x_{i0}, \end{array} \right. \end{equation*} where $^{cH}D^{\alpha} $ denotes the Caputo-Hadamard fractional derivative of order $ \alpha $, $ 1<\alpha\leq 2 $, $ i=1,2,\dots,n$, and $ f_{i}:\mathbb{R}_{+}\times\mathbb{R}^{m_i} \to \mathbb{R}^{m_i} $, $ g_{ij} : \mathbb{R}_{+}\times \mathbb{R}^{m_i}\times \mathbb{R}^{m_j} \to \mathbb{R}^{m_i} $ are given functions. Based on graph theory and the classical Lyapunov technique, we prove stability and uniform asymptotic stability under suitable sufficient conditions. We also provide an example to illustrate the obtained results. | ||
| کلیدواژه‌ها | ||
| Fractional differential equation؛ Caputo-Hadamard؛ Coupled systems on networks؛ Lyapunov function | ||
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