New results for convergence of Adomian's method applied to integral equations

Cherruault, Y.; Saccomandi, Giuseppe; Somé, Blaise

doi:10.1016/0895-7177(92)90009-a

Cited by 210 publications

(67 citation statements)

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“…In fact, our actual problem that we can face is the convergence of that approximate solution to the exact solution. The convergence analysis of the method was studied by many researchers, for example see [16,17]. Sufficient conditions for convergence are given in [18,19].…”

Section: Introductionmentioning

confidence: 99%

On Adomian's Decomposition Method for Solving a Fractional Advection-Dispersion Equation

Hikal¹,

Ibrahim²

2015

Int. J. of Pure and Appl. Math.

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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 α (0 < α ≤ 1). In addition, the space derivative orders are replaced by the alternative orders 0 < β ≤ 1 and 1 < γ ≤ 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.

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