IJPAM: Volume 104, No. 1 (2015)

ON ADOMIAN'S DECOMPOSITION METHOD FOR SOLVING
A FRACTIONAL ADVECTION-DISPERSION EQUATION

M.M. Hikal$^1$, M.A. Abu Ibrahim$^2$
$^1$Physics and Engineering Mathematics Department
Faculty of Engineering
Tanta University
Tanta, EGYPT
$^2$Mathematics Department
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 $\alpha$ ($0<\alpha\leq1$). In addition, the space derivative orders are replaced by the alternative orders $0<\beta\leq1$ and $1<\gamma\leq2$. 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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