奇摄动分数阶微分方程的渐近解（英文）  

ASYMPTOPIC SOLUTION FOR SINGULARLY PERTURBED FRACTIONAL ORDER DIFFERENTIAL EQUATION

作　　者：冯依虎[1] 莫嘉琪[2] 

机构地区：[1]亳州师范高等专科学校电子与信息工程系,安徽亳州236800 [2]安徽师范大学数学系,安徽芜湖241003

出　　处：《数学杂志》2016年第2期239-245,共7页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11202106);the Natural Science Foundation of the Education Department of Anhui Province(KJ2015A347;KJ2013B153)

摘　　要：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.In this paper, a class of initial value problem for the singularly perturbed fractional 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.

关 键 词：分数阶微分方程 奇摄动 渐近解 

分 类 号：O175.14[理学—数学]