A linearized stability theorem for nonlinear delay fractional differential equations
Classical Analysis and ODEs
2018-08-24 v1
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.
Cite
@article{arxiv.1706.03936,
title = {A linearized stability theorem for nonlinear delay fractional differential equations},
author = {Hoang The Tuan and Hieu Trinh},
journal= {arXiv preprint arXiv:1706.03936},
year = {2018}
}