奇摄动分数阶微分方程的渐近解

摘要

In this paper, a class of initial value problem for the singularly perturbed frac-tional order nonlinear differential equation is considered. Using the stretched variable method, a formal solution and its asymptotic expansion are constructed. And the uniformly valid asymptotic expansion of solution is proved by using the theory of differential inequalities. From obtained result, we know that this approximate solution possesses good accuracy.%本文研究了一类奇摄动非线性分数阶微分方程初值问题。利用伸长变量构造出解的形式展开式，并利用微分不等式理论，证明了解的一致有效的渐近式。所得的结果具有较好精度的近似解。