IJPAM: Volume 104, No. 1 (2015)
A FRACTIONAL ADVECTION-DISPERSION EQUATION



Faculty of Engineering
Tanta University
Tanta, EGYPT

Faculty of Science
Tanta University
Tanta, EGYPT
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
Year: 2015
Volume: 104
Issue: 1
Pages: 43 - 56
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This work is licensed under the Creative Commons Attribution International License (CC BY).