A study of forced oscillations via Hilfer fractional derivative
Palavras-chave:
Fractional Calculus, Forced oscillator, Hilfer fractional derivative, Dirac delta function.Resumo
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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28-09-2022
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MELO, S. de S. C.; OLIVEIRA, E. C. de. A study of forced oscillations via Hilfer fractional derivative. C.Q.D. - Revista Eletrônica Paulista de Matemática, Bauru, v. 22, n. 2, 2022. Disponível em: https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/339. Acesso em: 23 dez. 2024.
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Copyright (c) 2022 C.Q.D. - Revista Eletrônica Paulista de Matemática
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
