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Advances in Mathematical Physics
Volume 2015, Article ID 365328, 11 pages
http://dx.doi.org/10.1155/2015/365328
Research Article

Stability Criteria for Volterra Integrodynamic System

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60000, Pakistan

Received 28 July 2015; Revised 16 October 2015; Accepted 21 October 2015

Academic Editor: Ming Mei

Copyright © 2015 Nusrat Yasmin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study conditions under which the solutions of linear Volterra integrodynamic system of the form are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.