Abstract

MORALES-DELGADO, V.F.; GOMEZ-AGUILAR, J.F.  and  TANECO-HERNANDEZ, M.A.. Analytical solution of the time fractional diffusion equation and fractional convection-diffusion equation. Rev. mex. fis. [online]. 2019, vol.65, n.1, pp.82-88.  Epub Nov 09, 2019. ISSN 0035-001X.

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 α. 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 analytical solutions for the fractional order diffusion and convection-diffusion equations. The solutions obtained can be useful to understand the modeling of anomalous diffusion, subdiffusive systems and super-diffusive systems, transport processes, random walk and wave propagation phenomenon.

Keywords : Fractional calculus; Mittag-Leffler kernel; fractional conformable derivative; diffusion equation; 02.30.Uu; 04.20.Jb; 05.40.Fb; 05.60.-k.

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