Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation
In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general sol...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/390 |
| _version_ | 1828194064415064064 |
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| author | Andrey Zahariev Hristo Kiskinov |
| author_facet | Andrey Zahariev Hristo Kiskinov |
| author_sort | Andrey Zahariev |
| collection | DOAJ |
| description | In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system. |
| first_indexed | 2024-04-12T09:19:15Z |
| format | Article |
| id | doaj.art-540893befb424dbcaaba2f4b99c36bf8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-12T09:19:15Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-540893befb424dbcaaba2f4b99c36bf82022-12-22T03:38:42ZengMDPI AGMathematics2227-73902020-03-018339010.3390/math8030390math8030390Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear PerturbationAndrey Zahariev0Hristo Kiskinov1Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, BulgariaFaculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, BulgariaIn this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system.https://www.mdpi.com/2227-7390/8/3/390caputo fractional derivativeneutral linear fractional systemnonlinear perturbationasymptotic stability |
| spellingShingle | Andrey Zahariev Hristo Kiskinov Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation Mathematics caputo fractional derivative neutral linear fractional system nonlinear perturbation asymptotic stability |
| title | Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation |
| title_full | Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation |
| title_fullStr | Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation |
| title_full_unstemmed | Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation |
| title_short | Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation |
| title_sort | asymptotic stability of the solutions of neutral linear fractional system with nonlinear perturbation |
| topic | caputo fractional derivative neutral linear fractional system nonlinear perturbation asymptotic stability |
| url | https://www.mdpi.com/2227-7390/8/3/390 |
| work_keys_str_mv | AT andreyzahariev asymptoticstabilityofthesolutionsofneutrallinearfractionalsystemwithnonlinearperturbation AT hristokiskinov asymptoticstabilityofthesolutionsofneutrallinearfractionalsystemwithnonlinearperturbation |