New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay

Cemil Tunç, Yuanheng Wang, Osman Tunç and Jen-Chih Yao
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Cemil Tunç: Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
Yuanheng Wang: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Osman Tunç: Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan

Mathematics, 2021, vol. 9, issue 24, 1-20

Abstract: This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well as the boundedness of the perturbed system of IDDEs. In this paper, five new and improved fundamental qualitative results, which have less conservative conditions, are obtained on the mentioned fundamental properties of solutions. The technique used in the proofs depends on Lyapunov-Krasovski functionals (LKFs). In particular cases, three examples and their numerical simulations are provided as numerical applications of this paper. This paper provides new, extensive and improved contributions to the theory of IDDEs.

Keywords: non-linear system; IDDEs; constant delay; LKF; stability; instability; integrability; boundedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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