一类非线性奇摄动分数阶微分方程的渐近解

ASYMPTOPIC SOLUTION FOR A CLASS OF NONLINEAR SINGULARLY PERTURBED FRACTIONAL DIFFERENTIAL EQUATION

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,并由此得到解的渐近展开式.最后利用微分不等式理论,讨论了问题解的渐近性态,得到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 fractional differential equation is considered.Under the suitable conditions,the outer solution of the original problem is obtained,and then using the stretched variable,the composing expansion method and the expanding theory of power series,the boundary layer is constructed.Finally, using the theory of differential inequalities,the asymptotic behavior of solution for the problem is studied and the uniformly valid asymptotic estimation is given.