Electron. J. Diff. Equ., Vol. 2016 (2016), No. 58, pp. 1-22.

Stability of solutions to impulsive Caputo fractional differential equations

Ravi Agarwal, Snezhana Hristova, Donal O'Regan

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability of the solution are established. Some examples are given to illustrate the results.

Submitted December 16, 2015. Published February 25, 2016.
Math Subject Classifications: 34A34, 34A08, 34D20.
Key Words: Stability; Caputo derivative; Lyapunov functions; impulses; fractional differential equations.

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Ravi Agarwal
Department of Mathematics
Texas A&M University-Kingsville
Kingsville, TX 78363, USA
email: agarwal@tamuk.edu
Snezhana Hristova
Department of Applied Mathematics
Plovdiv University
Plovdiv, Bulgaria
email: snehri@gmail.com
Donal O'Regan
School of Mathematics
Statistics and Applied Mathematics
National University of Ireland
Galway, Ireland
email: donal.oregan@nuigalway.ie

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