ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Exponential Stability for Nonlinear Perturbed Time Scales Systems with Gr"{o}nwall-Bihari-Inequalities

Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 781--792 | DOI:10.5890/DNC.2022.12.015

Amira Ayari$^{1}$, Khaled Boukerrioua$^{1}$, Brahim Kilani$^{2}$

$^{1}$ Lanos Laboratory, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria

$^{2}$ Laboratory of Mathematics, Dynamics and Modelization, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000 Annaba, Algeria

Abstract

This paper focuses on the problem of exponential stability of certain classes of dynamic perturbed systems on time scales using time scale versions of some Gr\"{o}nwall-Bihari type inequalities.We prove under certain conditions on the nonlinear perturbations that the resulting perturbed nonlinear initial value problem still acquire exponential stable, if the associated linear system has already owned this property. The paper ends up with two illustrative examples to highlight the utility of our results.

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