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Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations

Authors :
Donal O'Regan
Ravi P. Agarwal
Snezhana Hristova
Source :
Symmetry, Vol 13, Iss 730, p 730 (2021), Symmetry; Volume 13; Issue 4; Pages: 730
Publication Year :
2021
Publisher :
MDPI AG, 2021.

Abstract

In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results.

Details

Language :
English
ISSN :
20738994
Volume :
13
Issue :
730
Database :
OpenAIRE
Journal :
Symmetry
Accession number :
edsair.doi.dedup.....22ba541eaf4dedf41fbf34fa8818178f