IJPAM: Volume 104, No. 1 (2015)
A FRACTIONAL ADVECTION-DISPERSION EQUATION
Physics and Engineering Mathematics Department
Faculty of Engineering
Faculty of Science
Abstract. In this paper, the Adomian's decomposition method (ADM) is considered to solve a fractional advection-dispersion model. This model can be represented if the first order derivative in time is replaced by the Caputo fractional derivative of order (). In addition, the space derivative orders are replaced by the alternative orders and . The obtained solutions are formulated in a convergent infinite series in terms of Mittage-Leffler functions. Finally, two illustrative examples are introduced to ensure the effectiveness of the used method.
Received: March 24, 2015
AMS Subject Classification: 34A08, 34K37
Key Words and Phrases: fractional calculus, Advection-dispersion equation, Adomian's decomposition method, Mittage-Leffler function
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DOI: 10.12732/ijpam.v104i1.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 43 - 56