A study of forced oscillations via Hilfer fractional derivative
The present study seeks to understand the forced oscillations through modeling via fractional differential equation, using the derivative according to Hilfer and representing the external force as a succession of delta Dirac functions. This formulation allows recovering the solutions according to C...
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| Format: | Article |
| Language: | Portuguese |
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UNESP
2022-09-01
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| Series: | CQD Revista Eletrônica Paulista de Matemática |
| Subjects: | |
| Online Access: | https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/339 |
| _version_ | 1797723964284338176 |
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| author | Silas de Sá Cavalcanti Melo Edmundo Capelas de Oliveira |
| author_facet | Silas de Sá Cavalcanti Melo Edmundo Capelas de Oliveira |
| author_sort | Silas de Sá Cavalcanti Melo |
| collection | DOAJ |
| description |
The present study seeks to understand the forced oscillations through modeling via fractional differential equation, using the derivative according to Hilfer and representing the external force as a succession of delta Dirac functions. This formulation allows recovering the solutions according to Caputo and Riemann-Liouville. The results obtained show that both Caputo and Riemann Liouville solutions coincide when we recover the entire order of the derivative. Also, by switching the order of the derivative it is possible to simulate damping.
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| first_indexed | 2024-03-12T10:10:26Z |
| format | Article |
| id | doaj.art-3e9d68eff0b5458fb04954560c59f165 |
| institution | Directory Open Access Journal |
| issn | 2316-9664 |
| language | Portuguese |
| last_indexed | 2024-03-12T10:10:26Z |
| publishDate | 2022-09-01 |
| publisher | UNESP |
| record_format | Article |
| series | CQD Revista Eletrônica Paulista de Matemática |
| spelling | doaj.art-3e9d68eff0b5458fb04954560c59f1652023-09-02T10:55:10ZporUNESPCQD Revista Eletrônica Paulista de Matemática2316-96642022-09-01222A study of forced oscillations via Hilfer fractional derivativeSilas de Sá Cavalcanti Melo0Edmundo Capelas de Oliveira1Instituto de Matemática, Estatística e Computação Científica - UNICAMP - Universidade Estadual de CampinasInstituto de Matemática, Estatística e Computação Científica - UNICAMP - Universidade Estadual de Campinas The present study seeks to understand the forced oscillations through modeling via fractional differential equation, using the derivative according to Hilfer and representing the external force as a succession of delta Dirac functions. This formulation allows recovering the solutions according to Caputo and Riemann-Liouville. The results obtained show that both Caputo and Riemann Liouville solutions coincide when we recover the entire order of the derivative. Also, by switching the order of the derivative it is possible to simulate damping. https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/339Fractional CalculusForced oscillatorHilfer fractional derivativeDirac delta function. |
| spellingShingle | Silas de Sá Cavalcanti Melo Edmundo Capelas de Oliveira A study of forced oscillations via Hilfer fractional derivative CQD Revista Eletrônica Paulista de Matemática Fractional Calculus Forced oscillator Hilfer fractional derivative Dirac delta function. |
| title | A study of forced oscillations via Hilfer fractional derivative |
| title_full | A study of forced oscillations via Hilfer fractional derivative |
| title_fullStr | A study of forced oscillations via Hilfer fractional derivative |
| title_full_unstemmed | A study of forced oscillations via Hilfer fractional derivative |
| title_short | A study of forced oscillations via Hilfer fractional derivative |
| title_sort | study of forced oscillations via hilfer fractional derivative |
| topic | Fractional Calculus Forced oscillator Hilfer fractional derivative Dirac delta function. |
| url | https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/339 |
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