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
Highlights
It is well known that, the advection-dispersion equation(ADE) is the mathemat-Received: March 24, 2015 §Correspondence author c 2015 Academic Publications, Ltd. url: www.acadpubl.euM.M
The diffusion and drift coefficient may be functions depending on the space variable ξ and the time τ to be in the form of FokkerPlanck equation(FPE)[3]
The authors in [9] presented a level IV fugacity model coupled to a dispersion-advection equation to simulate the environmental concentration of a pesticide in rice fields
Summary
Received: March 24, 2015 §Correspondence author c 2015 Academic Publications, Ltd. url: www.acadpubl.eu. Fractional derivatives play key role in modeling of particle transport in diffusion including the fractional Advection-dispersion equation(FADE)[3]. The authors in [12] developed practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain. A. El-Sayed et al [13] concerned with a model that describes the intermediate process between advection and dispersion via fractional derivative, an analytic approximate solution for that model is obtained by the powerful method called Adomian decomposition method(ADM). Adomian decomposition method (ADM) [14, 15] is a mathematical technique for solving large classes of ordinary and partial differential equations that gives an analytic approximate solution.
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