Solutions of Fractional Diffusion Equations and Cattaneo-Hristov Diffusion Model
The analytical solutions of the fractional diffusion equations in one and two-dimensional spaces have been proposed. The analytical solution of the Cattaneo-Hristov diffusion model with the particular boundary conditions has been suggested. In general, the numerical methods have been used to solve t...
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| Format: | Article |
| Language: | English |
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Etamaths Publishing
2019-03-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/1832 |
| Summary: | The analytical solutions of the fractional diffusion equations in one and two-dimensional spaces have been proposed. The analytical solution of the Cattaneo-Hristov diffusion model with the particular boundary conditions has been suggested. In general, the numerical methods have been used to solve the fractional diffusion equations and the Cattaneo-Hristov diffusion model. The Laplace and the Fourier sine transforms have been used to get the analytical solutions. The analytical solutions of the classical diffusion equations and the Cattaneo-Hristov diffusion model obtained when the order of the fractional derivative converges to 1 have been recalled. The graphical representations of the analytical solutions of the fractional diffusion equations and the Cattaneo-Hristov diffusion model have been provided. |
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| ISSN: | 2291-8639 |