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



Título del documento: Analytical solution of the time fractional diffusion equation and fractional convection-diffusion equation
Revista: Revista mexicana de física
Base de datos: PERIÓDICA
Número de sistema: 000429672
ISSN: 0035-001X
Autors: 1
2
1
Institucions: 1Universidad Autónoma de Guerrero, Facultad de Matemáticas, Chilpancingo, Guerrero. México
2Tecnológico Nacional de México, Cuernavaca, Morelos. México
Any:
Període: Ene-Feb
Volum: 65
Número: 1
País: México
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Analítico, teórico
Resumen en inglés 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
Disciplines Física y astronomía
Paraules clau: Física,
Cálculo fraccional,
Núcleo de Mittag-Leffler,
Derivada conformable fraccional,
Ecuación de difusión
Keyword: Physics,
Fractional calculus,
Mittag-Leffler kernel,
Fractional conformable derivative,
Diffusion equation
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