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Stability of scalar nonlinear fractional differential equations with linearly dominated delay

Hoang The Tuan and Stefan Siegmund

Abstract

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay equation is asymptotically stable and show that the asymptotic stability of the trivial solution is preserved under a small nonlinear Lipschitz perturbation of the fractional delay differential equation.

Acknowledgement

The research of Hoang The Tuan was supported by Vietnam Academy of Science and Technology under the grant DLTE00.01/20-21. This paper was done when he visited the Center for Dynamics at TU Dresden, Germany, with the support of Deutscher Akademischer Austauschdienst (DAAD). The authors thank Ninh Van Thu and Hieu Trinh for helpful discussions.

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Received: 2018-08-24
Revised: 2020-01-23
Published Online: 2020-02-27
Published in Print: 2020-02-25

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