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http://hdl.handle.net/10773/26362
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DC Field | Value | Language |
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dc.contributor.author | Agarwal, Ravi | pt_PT |
dc.contributor.author | Almeida, Ricardo | pt_PT |
dc.contributor.author | Hristova, Snezhana | pt_PT |
dc.contributor.author | O'Regan, Donal | pt_PT |
dc.date.accessioned | 2019-08-01T14:44:59Z | - |
dc.date.available | 2019-08-01T14:44:59Z | - |
dc.date.issued | 2019 | - |
dc.identifier.issn | 1056-2176 | pt_PT |
dc.identifier.uri | http://hdl.handle.net/10773/26362 | - |
dc.description.abstract | Practical stability properties of Caputo fractional delay differential equations is studied and, in particular, the case with state dependent delays is considered. These type of delays is a generalization of several types of delays such as constant delays, time variable delays, or distributed delays. In connection with the presence of a delay in a fractional differential equation and the application of the fractional generalization of the Razumikhin method, we give a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. Three types of derivatives for Lyapunov functions, the Caputo fractional derivative, the Dini fractional derivative, and the Caputo fractional Dini derivative, are applied to obtain several sufficient conditions for practical stability. An appropriate Razumikhin condition is applied. These derivatives allow the application of non-quadratic Lyapunov function for studying stability properties. We illustrate our theory on several nonlinear Caputo fractional differential equations with different types of delays | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | Dynamic Publishers, Inc | pt_PT |
dc.relation | UID/MAT/04106/2019 | pt_PT |
dc.rights | openAccess | pt_PT |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | pt_PT |
dc.subject | Functional-differential equations with fractional derivatives | pt_PT |
dc.subject | Stability | pt_PT |
dc.subject | Lyapunov functions | pt_PT |
dc.subject | State dependent delay | pt_PT |
dc.title | Caputo fractional differential equation with state dependent delay and practical stability | pt_PT |
dc.type | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.firstPage | 715 | pt_PT |
degois.publication.issue | 3 | pt_PT |
degois.publication.lastPage | 742 | pt_PT |
degois.publication.title | Dynamic Systems and Applications | pt_PT |
degois.publication.volume | 28 | pt_PT |
dc.relation.publisherversion | https://acadsol.eu/dsa/articles/28/3/11.pdf | pt_PT |
dc.identifier.doi | 10.12732/dsa.v28i3.11 | pt_PT |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[2019] Caputo fractional differential equation with state dependent delay and practical stability.pdf | 418.17 kB | Adobe PDF | View/Open |
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