Ravi Agarwal, Snezhana Hristova, Donal O'Regan
Abstract:
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 |
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Snezhana Hristova Department of Applied Mathematics Plovdiv University Plovdiv, Bulgaria email: snehri@gmail.com |
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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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