Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method
In this manuscript, we consider the first order neutral Volterra integro-differential equation (NVIDE) with delay argument. Firstly, we obtain novel sufficient conditions to establish the asymptotic behaviours of solutions of considered NVIDE using the Lyapunov method and present an example to demon...
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| Format: | Article |
| Language: | English |
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Kyrgyz Turkish Manas University
2021-04-01
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| Series: | MANAS: Journal of Engineering |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/1569149 |
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| author | Yener Altun |
| author_facet | Yener Altun |
| author_sort | Yener Altun |
| collection | DOAJ |
| description | In this manuscript, we consider the first order neutral Volterra integro-differential equation (NVIDE) with delay argument. Firstly, we obtain novel sufficient conditions to establish the asymptotic behaviours of solutions of considered NVIDE using the Lyapunov method and present an example to demonstrate the applicability of proposed method. Secondly, we get some numerical solutions for a particular case of considered NVIDE via the differential transformation method (DTM). The results of this manuscript are novel and they improve some existing ones in the literature. |
| format | Article |
| id | doaj-art-84af6eba124341239861101e2f3fae3b |
| institution | Kabale University |
| issn | 1694-7398 |
| language | English |
| publishDate | 2021-04-01 |
| publisher | Kyrgyz Turkish Manas University |
| record_format | Article |
| series | MANAS: Journal of Engineering |
| spelling | doaj-art-84af6eba124341239861101e2f3fae3b2025-02-03T12:07:27ZengKyrgyz Turkish Manas UniversityMANAS: Journal of Engineering1694-73982021-04-019Special 1495710.51354/mjen.8780661437Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform methodYener Altun0https://orcid.org/0000-0003-1073-5513YÜZÜNCÜ YIL ÜNİVERSİTESİIn this manuscript, we consider the first order neutral Volterra integro-differential equation (NVIDE) with delay argument. Firstly, we obtain novel sufficient conditions to establish the asymptotic behaviours of solutions of considered NVIDE using the Lyapunov method and present an example to demonstrate the applicability of proposed method. Secondly, we get some numerical solutions for a particular case of considered NVIDE via the differential transformation method (DTM). The results of this manuscript are novel and they improve some existing ones in the literature.https://dergipark.org.tr/en/download/article-file/1569149asymptotic behaviorlyapunov functionalnvidedtm |
| spellingShingle | Yener Altun Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method MANAS: Journal of Engineering asymptotic behavior lyapunov functional nvide dtm |
| title | Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method |
| title_full | Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method |
| title_fullStr | Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method |
| title_full_unstemmed | Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method |
| title_short | Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method |
| title_sort | asymptotic behaviours of the solutions of neutral type volterra integro differential equations and some numerical solutions via differential transform method |
| topic | asymptotic behavior lyapunov functional nvide dtm |
| url | https://dergipark.org.tr/en/download/article-file/1569149 |
| work_keys_str_mv | AT yeneraltun asymptoticbehavioursofthesolutionsofneutraltypevolterraintegrodifferentialequationsandsomenumericalsolutionsviadifferentialtransformmethod |