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http://hdl.handle.net/10773/38691
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DC Field | Value | Language |
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dc.contributor.author | Sousa, José Vanterler da C. | pt_PT |
dc.contributor.author | Oliveira, Daniela S. | pt_PT |
dc.contributor.author | Frederico, Gastão S. F. | pt_PT |
dc.contributor.author | Torres, Delfim F. M. | pt_PT |
dc.date.accessioned | 2023-07-17T09:33:48Z | - |
dc.date.available | 2023-07-17T09:33:48Z | - |
dc.date.issued | 2023 | - |
dc.identifier.issn | 0170-4214 | pt_PT |
dc.identifier.uri | http://hdl.handle.net/10773/38691 | - |
dc.description.abstract | We introduce a new version of $\psi$-Hilfer fractional derivative, on an arbitrary time scale. The fundamental properties of the new operator are investigated and, in particular, we prove an integration by parts formula. Using the Laplace transform and the obtained integration by parts formula, we then propose a $\psi$-Riemann-Liouville fractional integral on times scales. The applicability of the new operators is illustrated by considering a fractional initial value problem on an arbitrary time scale, for which we prove existence, uniqueness and controllability of solutions in a suitable Banach space. The obtained results are interesting and nontrivial even for particular choices: (i) of the time scale; (ii) of the order of differentiation; and/or (iii) function $\psi$; opening new directions of investigation. | pt_PT |
dc.description.sponsorship | This work was supported by Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico (FUNCAP) of Brazil, project BP4-00172-00054.02.00/20, and by Fundação para a Ciência e a Tecnologia (FCT) of Portugal, project UIDB/04106/2020 (CIDMA). | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | Wiley | pt_PT |
dc.relation | BP4-00172-00054.02.00/20 | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT | pt_PT |
dc.rights | restrictedAccess | pt_PT |
dc.subject | ψ-Hilfer fractional derivatives | pt_PT |
dc.subject | Fractional initial value problems | pt_PT |
dc.subject | Times scales | pt_PT |
dc.subject | Existence | pt_PT |
dc.subject | Uniqueness | pt_PT |
dc.subject | Controllability | pt_PT |
dc.title | Existence, uniqueness, and controllability for Hilfer differential equations on times scales | pt_PT |
dc.type | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.firstPage | 12378 | pt_PT |
degois.publication.issue | 12 | pt_PT |
degois.publication.lastPage | 12401 | pt_PT |
degois.publication.title | Mathematical Methods in the Applied Sciences | pt_PT |
degois.publication.volume | 46 | pt_PT |
dc.relation.publisherversion | https://doi.org/10.1002/mma.9183 | pt_PT |
dc.identifier.doi | 10.1002/mma.9183 | pt_PT |
dc.identifier.essn | 1099-1476 | pt_PT |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[533]Sousa_Oliveira_Frederico_Torres.pdf | 352.98 kB | Adobe PDF |
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