New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay
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-pe...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3317 |
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| author | Cemil Tunç Yuanheng Wang Osman Tunç Jen-Chih Yao |
| author_facet | Cemil Tunç Yuanheng Wang Osman Tunç Jen-Chih Yao |
| author_sort | Cemil Tunç |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:37:28Z |
| format | Article |
| id | doaj.art-b2ff888cce7742099f8a6bf890a6d2d6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:37:28Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b2ff888cce7742099f8a6bf890a6d2d62023-11-23T09:27:24ZengMDPI AGMathematics2227-73902021-12-01924331710.3390/math9243317New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant DelayCemil Tunç0Yuanheng Wang1Osman Tunç2Jen-Chih Yao3Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, TurkeyDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, TurkeyResearch Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, TaiwanThis 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.https://www.mdpi.com/2227-7390/9/24/3317non-linear systemIDDEsconstant delayLKFstabilityinstability |
| spellingShingle | Cemil Tunç Yuanheng Wang Osman Tunç Jen-Chih Yao New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay Mathematics non-linear system IDDEs constant delay LKF stability instability |
| title | New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay |
| title_full | New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay |
| title_fullStr | New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay |
| title_full_unstemmed | New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay |
| title_short | New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay |
| title_sort | new and improved criteria on fundamental properties of solutions of integro delay differential equations with constant delay |
| topic | non-linear system IDDEs constant delay LKF stability instability |
| url | https://www.mdpi.com/2227-7390/9/24/3317 |
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