摘要
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.
出处
《系统科学与数学》
CSCD
北大核心
2010年第12期1689-1694,共6页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金项目(40876010)
中国科学院知识创新工程重要方向项目(KZCX2-YW-Q03-08)
公益性行业科研专项(GYHY200806010)
LASG国家重点实验室专项经费
上海市教育委员会E-研究院建设计划项目(E03004)资助课题
关键词
非线性
分数阶微分方程
奇摄动
Nonlinear
fractional differential equation
singular perturbation
