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2014 Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative
José Francisco Gómez Aguilar, Margarita Miranda Hernández
Abstr. Appl. Anal. 2014: 1-8 (2014). DOI: 10.1155/2014/283019


An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as 0<β, γ1 for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters σx and σt are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.


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José Francisco Gómez Aguilar. Margarita Miranda Hernández. "Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative." Abstr. Appl. Anal. 2014 1 - 8, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022084
MathSciNet: MR3253575
Digital Object Identifier: 10.1155/2014/283019

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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