一类非线性非局部奇摄动分数阶微分方程Cauchy问题叠层解（英文）

The laminate layer solution to a class of Cauchy problem for nonlinear nonlocal singularly perturbed fractional order differential equation

研究了一类奇摄动非线性非局部分数阶微分方程Cauchy问题。首先求出了原问题的外部解。其次,利用伸长变量和合成展开法构造了初始层校正项。由此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,得到了原奇摄动非线性非局部分数阶微分方程Cauchy问题解的一致有效的渐近估计式。

A class of Cauchy problems for the nonlinear nonlocal singular perturbation fractional order differential equation is studied.Firstly,the outer solution of the original problem is obtained.Secondly,using the stretched variables and the composing expansion method,the initial layers are constructed.Finally,using the theory of differential inequality,the asymptotic behavior of the solution to original Cauchy problem of nonlinear nonlocal singular perturbation fractional order differential equation is studied and the uniformly valid asymptotic estimation is discussed.