Stability for coupled systems on networks with Caputo-Hadamard fractional derivative

Belbali, Hadjer; Benbachir, Maamar

doi:10.22124/jmm.2020.17303.1500

Stability for coupled systems on networks with Caputo-Hadamard fractional derivative

Document Type : Research Article

Authors

Hadjer Belbali ¹
Maamar Benbachir ²

¹ Laboratoire de Mathematiques et Sciences appliquees, University of Ghardaia, Algeriaa

² Faculty of Sciences, Saad Dahlab University, Blida, Algeria

10.22124/jmm.2020.17303.1500

Abstract

This paper discusses stability and uniform asymptotic stability of the trivial solution of the following coupled systems of fractional differential equations on networks

{\begin{cases} ^{c H} D^{α} x_{i} = f_{i} (t, x_{i}) + \sum_{j = 1}^{n} g_{i j} (t, x_{i}, x_{j}), & t > t_{0}, \\ x_{i} (t_{0}) = x_{i 0}, \end{cases}

where

^{c H} D^{α}

denotes the Caputo-Hadamard fractional derivative of order

α

1 < α \leq 2

i = 1, 2, \dots, n

, and

f_{i} : R_{+} \times R^{m_{i}} \to R^{m_{i}}

g_{i j} : R_{+} \times R^{m_{i}} \times R^{m_{j}} \to 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.

Keywords

Stability for coupled systems on networks with Caputo-Hadamard fractional derivative

Volume 9, Issue 1
January 2021
Pages 107-118

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Stability for coupled systems on networks with Caputo-Hadamard fractional derivative

Volume 9, Issue 1January 2021Pages 107-118

Files

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How to cite

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Volume 9, Issue 1
January 2021
Pages 107-118