一类分数阶微分方程初值问题的奇摄动  

Singular perturbation for a kind of fractional differential equations with initial value problem

作　　者：吴钦宽[1] 

机构地区：[1]南京工程学院数学研究所,江苏南京211167

出　　处：《高校应用数学学报（A辑）》2011年第1期41-45,共5页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11071205);江苏省自然科学基金(BK2008366)

摘　　要：研究了一类非线性分数阶微分方程加权初值问题的奇异摄动.在适当的条件下,首先求出了原问题的外部解,然后利用边界层函数法构造出解的初始层项,并由此得到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,得到了原问题解的一致有效的渐近估计式.A kind of weighted initial value problems for singularly perturbed nonlinear fractional differential equations is discussed.Under suitable conditions,the outer solution of the original problem is obtained.Then the boundary layer function method is used to construct the initial layer.Finally, using differential inequalities,the asymptotic behavior of the solutions for such problems is studied and the uniformly valid asymptotic estimation is discussed.

关 键 词：奇异摄动 非线性 分数阶微分方程 

分 类 号：O175.14[理学—数学]