Caputo fractional differential equations with non-instantaneous impulses and strict stability by Lyapunov functions

Author:

Agarwal Ravi1,Hristova Snehana2,O’Regan Donal3

Affiliation:

1. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, USA

2. Department of Applied Mathematics and Modeling, University of Plovdiv, Tzar Asen, Plovdiv, Bulgaria

3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Abstract

In this paper the statement of initial value problems for fractional differential equations with noninstantaneous impulses is given. These equations are adequate models for phenomena that are characterized by impulsive actions starting at arbitrary fixed points and remaining active on finite time intervals. Strict stability properties of fractional differential equations with non-instantaneous impulses by the Lyapunov approach is studied. An appropriate definition (based on the Caputo fractional Dini derivative of a function) for the derivative of Lyapunov functions among the Caputo fractional differential equations with non-instantaneous impulses is presented. Comparison results using this definition and scalar fractional differential equations with non-instantaneous impulses are presented and sufficient conditions for strict stability and uniform strict stability are given. Examples are given to illustrate the theory.

Publisher

National Library of Serbia

Subject

General Mathematics

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