Lyapunov functions and strict stability of Caputo fractional differential equations

Advances in Difference Equations

Ravi Agarwal¹  Snezhana Hristova²  Donal ORegan³ 

[1] Department of Mathematics, Texas A&M University-Kingsville, Kingsville, USA;NAAM Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;Plovdiv University, Plovdiv, Bulgaria

关键词: strict stability;    Lyapunov functions;    Caputo derivatives;    fractional differential equations;    34A34;    34A08;    34D20;   

DOI  :  10.1186/s13662-015-0674-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY