A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations
In this article, the authors obtain some clear assumptions for the asymptotic stability (AS) and boundedness (B) of solutions of non-linear retarded Volterra integro-differential equations (VIDEs) of first order by constructing a new Lyapunov functional (LF). The results obtained are new and differ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X17300354 |
| _version_ | 1818995223477354496 |
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| author | Cemil Tunç Sizar Abid Mohammed |
| author_facet | Cemil Tunç Sizar Abid Mohammed |
| author_sort | Cemil Tunç |
| collection | DOAJ |
| description | In this article, the authors obtain some clear assumptions for the asymptotic stability (AS) and boundedness (B) of solutions of non-linear retarded Volterra integro-differential equations (VIDEs) of first order by constructing a new Lyapunov functional (LF). The results obtained are new and differ from those found in the literature, and they also contain and improve a result found in the literature under more less restrictive conditions. We establish an example and give a discussion to indicate the applicability of the weaker conditions obtained. We also employ MATLAB-Simulink to display the behaviors of the orbits of the (VIDEs) considered. Keywords: Nonlinear, Volterra integro-differential equations, First order, Asymptotic stability, Boundedness, Lyapunov functional, MSC: 34D05, 34K20, 45J05 |
| first_indexed | 2024-12-20T21:10:26Z |
| format | Article |
| id | doaj.art-0ae4e05c05084603ab74f680798e5b3c |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-20T21:10:26Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-0ae4e05c05084603ab74f680798e5b3c2022-12-21T19:26:32ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2017-10-01254363368A remark on the stability and boundedness criteria in retarded Volterra integro-differential equationsCemil Tunç0Sizar Abid Mohammed1Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, 65080, Van, Turkey; Corresponding author.Department of Mathematics,College of Basic Education,University of Duhok Zakho Street 38, 1006 AJ, Duhok, IraqIn this article, the authors obtain some clear assumptions for the asymptotic stability (AS) and boundedness (B) of solutions of non-linear retarded Volterra integro-differential equations (VIDEs) of first order by constructing a new Lyapunov functional (LF). The results obtained are new and differ from those found in the literature, and they also contain and improve a result found in the literature under more less restrictive conditions. We establish an example and give a discussion to indicate the applicability of the weaker conditions obtained. We also employ MATLAB-Simulink to display the behaviors of the orbits of the (VIDEs) considered. Keywords: Nonlinear, Volterra integro-differential equations, First order, Asymptotic stability, Boundedness, Lyapunov functional, MSC: 34D05, 34K20, 45J05http://www.sciencedirect.com/science/article/pii/S1110256X17300354 |
| spellingShingle | Cemil Tunç Sizar Abid Mohammed A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations Journal of the Egyptian Mathematical Society |
| title | A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations |
| title_full | A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations |
| title_fullStr | A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations |
| title_full_unstemmed | A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations |
| title_short | A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations |
| title_sort | remark on the stability and boundedness criteria in retarded volterra integro differential equations |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X17300354 |
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