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Article

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

by
Cemil Tunç
1,†,
Yuanheng Wang
2,*,†,
Osman Tunç
3,† and
Jen-Chih Yao
4,†
1
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
2
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
3
Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
4
Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2021, 9(24), 3317; https://doi.org/10.3390/math9243317
Submission received: 16 November 2021 / Revised: 10 December 2021 / Accepted: 14 December 2021 / Published: 20 December 2021
(This article belongs to the Special Issue New Advances in Functional Analysis)
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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 non-linear system; IDDEs; constant delay; LKF; stability; instability; integrability; boundedness

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MDPI and ACS Style

Tunç, C.; Wang, Y.; Tunç, O.; Yao, J.-C. New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay. Mathematics 2021, 9, 3317. https://doi.org/10.3390/math9243317

AMA Style

Tunç C, Wang Y, Tunç O, Yao J-C. New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay. Mathematics. 2021; 9(24):3317. https://doi.org/10.3390/math9243317

Chicago/Turabian Style

Tunç, Cemil, Yuanheng Wang, Osman Tunç, and Jen-Chih Yao. 2021. "New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay" Mathematics 9, no. 24: 3317. https://doi.org/10.3390/math9243317

APA Style

Tunç, C., Wang, Y., Tunç, O., & Yao, J.-C. (2021). New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay. Mathematics, 9(24), 3317. https://doi.org/10.3390/math9243317

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