Analytical solution of the time fractional diffusion equation and fractional convection-diffusion equation

• V.F. Morales-Delgado ^[1] ; J.F. Gómez-Aguilar ^[2] ; M.A. Taneco-Hernández ^[1]
  1. [1] Universidad Autónoma de Guerrero

     Universidad Autónoma de Guerrero

     México

     
  2. [2] Tecnológico Nacional de México

     Tecnológico Nacional de México

     México

     
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 65, Nº. 1, 2019, págs. 82-88
• Idioma: inglés
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• Resumen

  • In this paper, we obtain analytical solutions for the time-fractional diffusion and time-fractional convection-diffusion equations. These equations are obtained from the standard equations by replacing the time derivative with a fractional derivative of order $\alpha$. Fractional operators of type Liouville-Caputo, Atangana-Baleanu-Caputo, fractional conformable derivative in Liouville-Caputo sense and Atangana-Koca-Caputo were used to model diffusion and convection-diffusion equation. The Laplace and Fourier transforms were applied to obtain the analytical solutions for the fractional order diffusion and convection-diffusion equations. The solutions obtained can be useful to understand the modeling of anomalous diffusive, subdiffusive systems and super-diffusive systems, transport processes, random walk and wave propagation phenomenon.