Applications of Lyapunov Functions to Caputo Fractional Differential Equations

Ravi Agarwal, Snezhana Hristova and Donal O’Regan
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Ravi Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
Snezhana Hristova: Department of Applied Mathematics and Modeling, University of Plovdiv, Tzar Asen 24, 4000 Plovdiv, Bulgaria
Donal O’Regan: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 CF50 Galway, Ireland

Mathematics, 2018, vol. 6, issue 11, 1-17

Abstract: One approach to study various stability properties of solutions of nonlinear Caputo fractional differential equations is based on using Lyapunov like functions. A basic question which arises is the definition of the derivative of the Lyapunov like function along the given fractional equation. In this paper, several definitions known in the literature for the derivative of Lyapunov functions among Caputo fractional differential equations are given. Applications and properties are discussed. Several sufficient conditions for stability, uniform stability and asymptotic stability with respect to part of the variables are established. Several examples are given to illustrate the theory.

Keywords: stability; Caputo derivative; Lyapunov functions; fractional differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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