Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems

Atangana Abdon; Goufo Emile Franc Doungmo

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Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems

机译：匹配渐近方法扩展到分数阶边界层问题

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We were concerned with the description of the boundary layers problems within the scope of fractional calculus. However, we will note that one of the main methods used to solve these problems is the matched asymptotic method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the matched asymptotic method to the scope of fractional derivative, we proposed a relatively new derivative called the beta-derivative. We presented some useful information for this operator. With the reward of this operator, we presented the idea of matched asymptotic method in finding solutions of the fractional boundary layers problems. The method was illustrated with an example.

机译：我们关注分数微积分范围内边界层问题的描述。但是，我们将注意到，用于解决这些问题的主要方法之一是匹配渐近方法。我们应该提到，这不能通过现有的分数导数定义来实现，因为它们不遵循链式规则。为了使匹配渐近方法适应分数导数的范围，我们提出了一种相对较新的导数，称为β导数。我们为该运算符提供了一些有用的信息。有了这个算子的奖励，我们提出了匹配渐近方法的思想，以寻找分数边界层问题的解。举例说明了该方法。

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《Mathematical Problems in Engineering》 |2014年第21期|107535.1-107535.7|共7页
作者
Atangana Abdon; Goufo Emile Franc Doungmo;
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Univ Orange Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, ZA-9300 Bloemfontein, South Africa.;

Univ S Africa, Dept Math Sci, ZA-0003 Florida, South Africa.;

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1. Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems [J] . AbdonAtangana, Emile FrancDoungmo Goufo Mathematical Problems in Engineering: Theory, Methods and Applications . 2014,第2期

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2. Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems [J] . AbdonAtangana, Emile FrancDoungmo Goufo Mathematical Problems in Engineering: Theory, Methods and Applications . 2014,第1期

机译：匹配渐近方法扩展到分数阶边界层问题
3. Generalized perfectly matched layer-an extension of Berenger's perfectly matched layer boundary condition [J] . Jiayuan Fang, Zhonghua Wu IEEE Microwave and Guided Wave Letters . 1995,第12期

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7. Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems [O] . Abdon Atangana, Emile Franc Doungmo Goufo 2014

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Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems

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