Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives
Abstract This work mainly investigates the separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio fractional derivatives. An inequality ensuring the positivity of the fractional derivative at a given point is derived, by which the sufficient conditions for the separatio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-04-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02632-x |
| _version_ | 1818035577665093632 |
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| author | Wenyong Zhong Lanfang Wang Thabet Abdeljawad |
| author_facet | Wenyong Zhong Lanfang Wang Thabet Abdeljawad |
| author_sort | Wenyong Zhong |
| collection | DOAJ |
| description | Abstract This work mainly investigates the separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio fractional derivatives. An inequality ensuring the positivity of the fractional derivative at a given point is derived, by which the sufficient conditions for the separation of solutions are obtained. The comparison principle and the inequality for the fractional derivatives of convex functions are obtained, by which the approach of the convex Lyapunov functions is extended effectively to establish the criteria for the stability of solutions in the context of Caputo–Fabrizio fractional derivatives. Applications of the main results are illustrated by using examples. |
| first_indexed | 2024-12-10T06:57:16Z |
| format | Article |
| id | doaj.art-1c7549fbf18b4f7690bfba855ea7802e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T06:57:16Z |
| publishDate | 2020-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-1c7549fbf18b4f7690bfba855ea7802e2022-12-22T01:58:24ZengSpringerOpenAdvances in Difference Equations1687-18472020-04-012020111510.1186/s13662-020-02632-xSeparation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivativesWenyong Zhong0Lanfang Wang1Thabet Abdeljawad2College of Mathematics and Statistics, Jishou UniversityCollege of Mathematics and Statistics, Jishou UniversityDepartment of Mathematics and General Sciences, Prince Sultan UniversityAbstract This work mainly investigates the separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio fractional derivatives. An inequality ensuring the positivity of the fractional derivative at a given point is derived, by which the sufficient conditions for the separation of solutions are obtained. The comparison principle and the inequality for the fractional derivatives of convex functions are obtained, by which the approach of the convex Lyapunov functions is extended effectively to establish the criteria for the stability of solutions in the context of Caputo–Fabrizio fractional derivatives. Applications of the main results are illustrated by using examples.http://link.springer.com/article/10.1186/s13662-020-02632-xCaputo–Fabrizio derivativesNonlinear systemsStabilitySeparation of solutionsConvex Lyapunov functions |
| spellingShingle | Wenyong Zhong Lanfang Wang Thabet Abdeljawad Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives Advances in Difference Equations Caputo–Fabrizio derivatives Nonlinear systems Stability Separation of solutions Convex Lyapunov functions |
| title | Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives |
| title_full | Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives |
| title_fullStr | Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives |
| title_full_unstemmed | Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives |
| title_short | Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives |
| title_sort | separation and stability of solutions to nonlinear systems involving caputo fabrizio derivatives |
| topic | Caputo–Fabrizio derivatives Nonlinear systems Stability Separation of solutions Convex Lyapunov functions |
| url | http://link.springer.com/article/10.1186/s13662-020-02632-x |
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