New and improved criteria on qualitative results for functional-differential systems

Osman Tunc; Seenith Sivasundaram; Ozkan Atan; Cemil Tunc

Osman Tunc Baskale Vocational School ,\\ Van Yuzuncu Yil University, 65080, Campus, Van – Turkey
Seenith Sivasundaram College of Science,Engineering and Mathematics,\\ Daytona Beach, FL 32114, USA
Ozkan Atan Faculty of Engineering, Van Yuzuncu Yil University, 65080, Campus, Van – Turkey
Cemil Tunc Van Yuzuncu Yil University, 65080, Campus Van-Turkey

Abstract

In this paper, certain systems of functional differential equations (FDEs) with multiple constant delays are considered. Using the Lyapunov – Krasovski\v{i} functionals (LKFs), new and improved Lyapunov-Krasovski\v{i} type fundamental criteria of uniformly stability (US), uniformly asymptotically stability (UAS), integrability and boundedness of solutions are obtained, respectively. Here, four new theorems are presented as complements of some related results in the past literature. Finally, we verify our results by giving two numerical examples with plots of paths of solutions.