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 � (0 < � ≤ 1). In addition, the space derivative orders are replaced by the alternative orders 0 < � ≤ 1 and 1 < ≤ 2. 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. AMS Subject Classification: 34A08, 34K37
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