Affiliation:
1. Department of Mathematics , Shanghai University , Shanghai 200444 , China
Abstract
Abstract
In this article, we focus on stability and ψ-algebraic decay (algebraic decay in the sense of ψ-function) of the equilibrium to the nonlinear ψ-fractional ordinary differential system. Before studying the nonlinear case, we show the stability and decay for linear system in more detail. Then we establish the linearization theorem for the nonlinear system near the equilibrium and further determine the stability and decay rate of the equilibrium. Such discussions include two cases, one with ψ-Caputo fractional derivative, another with ψ-Riemann–Liouville derivative, where the latter is a bit more complex than the former. Besides, the integral transforms are also provided for future studies.
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
Cited by
15 articles.
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