分数阶双参数高阶非线性扰动模型的渐近解  

Asymptotic Solution for Fractional⁃Order 2⁃Parameter High⁃Order Nonlinear Perturbed Models

作　　者：徐建中 莫嘉琪 XU Jianzhong;MO Jiaqi(Department of Electronics and Information Engineering,Bozhou University,Bozhou,Anhui 236800,P.R.China;School of Mathematics&Statistics,Anhui Normal University,Wuhu,Anhui 241003,P.R.China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800 [2]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《应用数学和力学》2020年第6期679-686,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(41275062);安徽省教育厅自然科学重点基金(KJ2019A1303);安徽省高校优秀青年人才支持计划项目(gxyq2018116)。

摘　　要：研究了一类高阶非线性分数阶扰动微分模型.在适当的条件下,首先利用扰动方法求出了原问题的外部解,然后用伸长变量、合成展开和幂级数理论构造出解的第一、第二边界层校正项,并得到了解的形式渐近展开式.最后利用微分不等式理论,研究了问题解的渐近性态,并证明了问题解渐近估计式的一致有效性.A class of nonlinear fractional⁃order perturbed higher⁃order differential models was considered.Firstly,under suitable conditions,the outer solution to the original problem was obtained with the perturbation method.Then by means of the stretched variable,the composite expansion method and the theory of power series,the first and second boundary layer correc⁃tion terms were constructed and the formal asymptotic expansion was obtained.Finally,with the theory of differential inequalities the asymptotic behavior of the solution to the problem was studied and the uniform validity of the asymptotic estimate expression was proved.

关 键 词：边界层 分数阶微分模型 扰动 

分 类 号：O175.29[理学—数学]