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

被引：13

作者：

Tunc, Cemil ^{[1
]}

Wang, Yuanheng ^{[2
]}

Tunc, Osman ^{[3
]}

Yao, Jen-Chih ^{[4
]}

机构：

[1] Van Yuzuncu Yil Univ, Fac Sci, Dept Math, TR-65080 Van, Turkey

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[3] Van Yuzuncu Yil Univ, Dept Comp Programing, Baskale Vocat Sch, TR-65080 Van, Turkey

[4] China Med Univ, China Med Univ Hosp, Res Ctr Interneural Comp, Taichung 404332, Taiwan

来源：

MATHEMATICS | 2021年 / 9卷 / 24期

基金：

中国国家自然科学基金;

关键词：

non-linear system; IDDEs; constant delay; LKF; stability; instability; integrability; boundedness; STABILITY; SYSTEMS;

D O I：

10.3390/math9243317

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：20

共 50 条

[21] ON THE FUNDAMENTAL ANALYSES OF SOLUTIONS TO NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF SECOND ORDER [J].

Tuno, Osman .

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2023, 24 (01) :17-32

[22] Stability Analysis of Solutions for a Kind of Integro-Differential Equations with a Delay [J].

Zhao, Jing ;

Meng, Fanwei .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2018, 2018

[23] Existence of solutions for neutral integro-differential equations with state-dependent delay [J].

Fu, Xianlong ;

Huang, Rong .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 :743-759

[24] On the existence of periodic solutions of third order delay differential equations [J].

Erdur, Sultan ;

Tunc, Cemil .

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2023, 11 (02) :319-331

[25] Numerical solutions of stochastic delay integro-differential equations by block pulse functions [J].

Jiang, Guo ;

Chen, Yuanqin ;

Ying, Jiayi .

APPLIED NUMERICAL MATHEMATICS, 2025, 208 :214-230

[26] EXISTENCE, UNIQUENESS AND REGULARITY OF SOLUTIONS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY [J].

Liang, Yixing ;

Fan, Zhenbin ;

Li, Gang .

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (02) :623-641

[27] Existence and Uniqueness of Solutions for Abstract Integro-differential Equations with State-Dependent Delay and Applications [J].

Hernandez, Eduardo ;

Rolnik, Vanessa ;

Ferrari, Thauana M. .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (03)

[28] Solution estimates to Caputo proportional fractional derivative delay integro-differential equations [J].

Tunc, Osman ;

Tunc, Cemil .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (01)

[29] Stability of Solutions of Delay Differential Equations [J].

Yskak T. .

Siberian Advances in Mathematics, 2023, 33 (3) :253-260

[30] Multiple periodic solutions for delay differential equations with a general piecewise constant argument [J].

Ding, Hui-Sheng ;

Wang, Hong ;

N'Guerekata, Gaston M. .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (04) :1960-1970

← 1 2 3 4 5 →