文章基本信息

标题：Lyapunov functions and strict stability of Caputo fractional differential equations
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作者：Ravi Agarwal ; Snezhana Hristova ; Donal O’Regan 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：346
DOI：10.1186/s13662-015-0674-5
语种：English
出版社：Hindawi Publishing Corporation
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.
关键词：strict stability ; Lyapunov functions ; Caputo derivatives ; fractional differential equations