Linearized Asymptotic Stability for Fractional Differential Equations

By Nguyen Dinh Cong, Thai Son Doan, Stefan Siegmund, Hoang The Tuan. 2015

69 citations recorded by the source corpus.

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector $\{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\}$ where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/01dafc6763cca8b197d89b6a3f748d991fef5c40

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Nguyen Dinh Cong
2. Hieu Minh Trinh
3. Hoang The Tuan

In Modeling and Simulation

1. Nguyen Dinh Cong
2. Hieu Minh Trinh
3. Hoang The Tuan

In Numerical Analysis

1. Nguyen Dinh Cong
2. Hieu Minh Trinh
3. Hoang The Tuan

Citations in the corpus

• On asymptotic properties of solutions to fractional differential equations (2018, methodology): “In [10], the authors give a linearized stability theorem for the trivial solution of (8) as follows.”