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arXiv · 1706.03936

A linearized stability theorem for nonlinear delay fractional differential equations

Hoang The Tuan·Hieu Trinh
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Abstract

In this paper, we prove a theorem of linearized asymptotic stability for fractional differential equations with a time delay. More precisely, using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first method), we show that an equilibrium of a nonlinear Caputo fractional differential equation with a time delay is asymptotically stable if its linearization at the equilibrium is asymptotically stable. Our approach based on a technique which converts the linear part of the equation into a diagonal one. Then using properties of generalized Mittag-Leffler functions, the construction of an associated Lyapunov--Perron operator and the Banach contraction mapping theorem, we obtain the desired result.

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Hoang The Tuan, Hieu Trinh. 2017-06-13. A linearized stability theorem for nonlinear delay fractional differential equations. https://doi.org/10.1109/tac.2018.2791485

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