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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Qualitative Aspects for Volterra Integro-Dynamic Matrix Sylvester Impulsive System on Time Scales

Journal of Applied Nonlinear Dynamics 13(1) (2024) 65--81 | DOI:10.5890/JAND.2024.03.006

A. Sreenivasulu$^{1}$, B. V. Appa Rao$^2$

$^1$ Department of Science and Humanities, MLR Institute of Technology, Dundigal, Hyderabad- 500043, Telangana, India

$^2$ Department of Engineering Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, 522302, Andhra Pradesh, India

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Abstract

In this paper, we establish the asymptotic stability and boundedness of the Volterra integro-dynamic matrix Sylvester impulsive system on time scales. First, we convert the linear Volterra integro-dynamic matrix Sylvester impulsive system on time scale to an equivalent Kronecker product Volterra integro-dynamic impulsive system on time scales using vectorization operator. Then, we obtaine the results for asymptotic stability and boundedness of a time-varying Volterra integro-dynamic matrix Sylvester impulsive system on time scales in which the coefficient matrix is not necessarily stable. We generalize to a time scale some known properties concerning the asymptotic stability and boundedness from the continuous version. Finally, we’ve given some numerical and theoretical examples of the way those advanced analytical consequences may be applied.

Acknowledgments

The authors would like to express their sincere thanks to the editor and anonymous reviewers for constructive comments and suggestions to improve the quality of this paper.

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