Abstract
One of the main properties studied in the qualitative theory of differential equations is the stability of solutions. The stability of fractional order systems is quite recent. There are several approaches in the literature to study stability, one of which is the Lyapunov approach. However, the Lyapunov approach to fractional differential equations causes many difficulties. In this paper a new definition (based on the Caputo fractional Dini derivative) for the derivative of Lyapunov functions to study a nonlinear Caputo fractional differential equation is introduced. Comparison results using this definition and scalar fractional differential equations are presented, and sufficient conditions for strict stability and uniform strict stability are given. Examples are presented to illustrate the theory.
| Original language | English |
|---|---|
| Article number | 346 |
| Pages (from-to) | 1-20 |
| Number of pages | 20 |
| Journal | Advances in Difference Equations |
| Volume | 2015 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Dec 2015 |
Keywords
- Caputo derivatives
- Lyapunov functions
- fractional differential equations
- strict stability