| 非线性分数阶微分方程的奇摄动 |
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| 引用本文： | 莫嘉琪.非线性分数阶微分方程的奇摄动[J].应用数学学报,2006,29(6):1085-1090. |
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| 作者姓名： | 莫嘉琪 |
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| 作者单位： | 安徽师范大学数学系,芜湖,241000;上海高校计算科学院,E-研究院上海交通大学研究所,上海,200240;湖州师范学院数学系,湖州,313000;上海高校计算科学院,E-研究院上海交通大学研究所,上海,200240 |
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| 基金项目： | 国家自然科学基金;国家重点基础研究发展计划(973计划);中国科学院基金;上海教育委员会E-研究院建设计划项目 |
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| 摘 要： | 研究了—类奇摄动非线性分数阶微分方程Cauchy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．
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| 关 键 词： | 非线性 分数阶微分方程 奇摄动 |
| 收稿时间： | 2005-06-03 |
| 修稿时间： | 2005-06-032005-11-25 |
Singular Perturbation of Nonlinear Fractional Differential Equation |
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| MO JIAQI.Singular Perturbation of Nonlinear Fractional Differential Equation[J].Acta Mathematicae Applicatae Sinica,2006,29(6):1085-1090. |
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| Authors: | MO JIAQI |
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| Institution: | 1Department of Mathematics, Anhui Normal University, Wuhu 241000;2Department of Mathematics, Huzhou Teachers College, Huzhou 313000;3Division of Computational Science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 200240 |
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| Abstract: | A class of the Cauchy problem for singularly perturbed nonlinear fractional differential equation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial 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 discussed. |
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| Keywords: | nonlinear fractional diflFerential equation singular perturbation |
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