Numerical algorithms considering a dimensional correction parameter on the fractional order diffusion equation

Authors

  • Jhoab Pessoa de Negreiros UERJ - Universidade do Estado do Rio de Janeiro
  • Carlos Antonio de Moura Instituto de Matemática e Estatística - UERJ - Universidade do Estado do Rio de Janeiro
  • Cristiane Oliveira de Faria Instituto de Matemática e Estatística - UERJ - Universidade do Estado do Rio de Janeiro

Keywords:

Fractional diffusion equation, Dimensional correction, Finite differences approximation, Riemman-Liouville, Caputo-Fabrizio and Katugampola fractional derivatives.

Abstract

We deal with a generalization for the constant coefficient onedimensional fractional diffusion equation by inserting the dimensional correction parameter 𝜏 in the model, as proposed in (GÓMEZ-AGUILAR et al., 2012). The fractional time variation is simulated by the Riemann-Liouville, Caputo-Fabrizio and Katugampola derivatives in order to compare each of these operators behavior. Numerical results drawn for the dimensionalized fractional diffusion equation are also compared with those obtained for the same equations when the dimension constraint was not taken into account.

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Published

2022-09-28

How to Cite

NEGREIROS, J. P. de; MOURA, C. A. de; FARIA, C. O. de. Numerical algorithms considering a dimensional correction parameter on the fractional order diffusion equation. 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/324. Acesso em: 13 nov. 2024.

Issue

v.22, n.2 - Edição Brazilian Symposium on Fractional Calculus – Set/2022

Section

Artigos de Pesquisa

License

Copyright (c) 2022 C.Q.D. - Revista Eletrônica Paulista de Matemática

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