分数阶双参数奇摄动非线性微分方程的渐近解

Asymptotic Solution for the Fractional Order Singularly Perturbed Nonlinear Differential Equation with Two Parameters

研究了一类奇摄动非线性分数阶微分方程边值问题.在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量、合成展开法和幂级数展开理论构造出解的边界层项,并得到了解的形式渐近展开式.最后利用微分不等式理论,讨论了问题解的渐近性态,证明了原问题解的一致有效的渐近估计式.

A class of the boundary value problem for the nonlinear singularly perturbed frac- tional order differential equation is considered. Under the suitable conditions, firstly, the outer solution of the original problem is obtained. Secondly, using the stretched variable, the com- posing expansion method and expanding theory of power series, the boundary layers are con- structed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the problem is studied and the uniformly valid asymptotic estimation is proved.