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Article

New Fundamental Results on the Continuous and Discrete Integro-Differential Equations

by
Osman Tunç
1,†,
Cemil Tunç
2,†,
Jen-Chih Yao
3 and
Ching-Feng Wen
4,5,*
1
Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
2
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
3
Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
4
Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
5
Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2022, 10(9), 1377; https://doi.org/10.3390/math10091377
Submission received: 23 March 2022 / Revised: 17 April 2022 / Accepted: 18 April 2022 / Published: 20 April 2022
(This article belongs to the Special Issue Applied Functional Analysis and Applications)
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Abstract

This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method and the Lyapunov–Razumikhin method (LRM), uniform asymptotic stability (UAS), uniform stability (US), integrability and boundedness of solutions as well as exponential stability (ES) and instability of solutions are discussed. In this paper, five new theorems and a corollary are given and three numerical applications are provided with their simulations. With this work, we aim to make new contributions to the theory of the continuous and discrete integro-differential equations.
Keywords: nonlinear system of IDEs; stability; instability; integrability; boundedness at infinity; LKF nonlinear system of IDEs; stability; instability; integrability; boundedness at infinity; LKF

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MDPI and ACS Style

Tunç, O.; Tunç, C.; Yao, J.-C.; Wen, C.-F. New Fundamental Results on the Continuous and Discrete Integro-Differential Equations. Mathematics 2022, 10, 1377. https://doi.org/10.3390/math10091377

AMA Style

Tunç O, Tunç C, Yao J-C, Wen C-F. New Fundamental Results on the Continuous and Discrete Integro-Differential Equations. Mathematics. 2022; 10(9):1377. https://doi.org/10.3390/math10091377

Chicago/Turabian Style

Tunç, Osman, Cemil Tunç, Jen-Chih Yao, and Ching-Feng Wen. 2022. "New Fundamental Results on the Continuous and Discrete Integro-Differential Equations" Mathematics 10, no. 9: 1377. https://doi.org/10.3390/math10091377

APA Style

Tunç, O., Tunç, C., Yao, J.-C., & Wen, C.-F. (2022). New Fundamental Results on the Continuous and Discrete Integro-Differential Equations. Mathematics, 10(9), 1377. https://doi.org/10.3390/math10091377

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