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

Osman Tunç, Cemil Tunç, Jen-Chih Yao and Ching-Feng Wen
Additional contact information
Osman Tunç: Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
Cemil Tunç: Department of Mathematics, Faculty of Sciences, 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
Ching-Feng Wen: Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Mathematics, 2022, vol. 10, issue 9, 1-18

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/9/1377/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/9/1377/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:9:p:1377-:d:797979

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().