一类奇摄动分数阶微分方程的渐近解

Asymptotic solution for a class of singularly perturbed fractional differential equations

讨论了一类奇摄动分数阶微分方程边值问题。在适当假设条件下,先求出该问题的外部解,再运用双参数展开理论构造出边界层矫正项,得到解的形式渐近展开式,最后运用极值原理进行余项估计。

A class of the boundary value problem for the singularly perturbed fractional differential equation is considered.Under the suitable conditions,firstly,the outer solution of the original problem is obtained by Volterra integral equation;secondly,using the two-parameters expanding theory of power series,the boundary layers are constructed;finally,by using the extremum principle of fractional differential equation,the remainder is estimated.