| 奇摄动分数阶微分方程的渐近解 |
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| 引用本文： | 冯依虎,莫嘉琪.奇摄动分数阶微分方程的渐近解[J].数学杂志,2016,36(2):239-245. |
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| 作者姓名： | 冯依虎 莫嘉琪 |
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| 作者单位： | 亳州师范高等专科学校电子与信息工程系, 安徽 亳州 236800,安徽师范大学数学系, 安徽 芜湖 241003 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (11202106);Natural Science Foundation of the Education Department of Anhui Province (KJ2015A347;KJ2013B153) |
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| 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.
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| 关 键 词： | 分数阶微分方程 奇摄动 渐近解 |
| 收稿时间： | 2014/11/17 0:00:00 |
| 修稿时间： | 2015/3/23 0:00:00 |
ASYMPTOPIC SOLUTION FOR SINGULARLY PERTURBED FRACTIONAL ORDER DIFFERENTIAL EQUATION |
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| FENG Yi-hu and MO Jia-qi.ASYMPTOPIC SOLUTION FOR SINGULARLY PERTURBED FRACTIONAL ORDER DIFFERENTIAL EQUATION[J].Journal of Mathematics,2016,36(2):239-245. |
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| Authors: | FENG Yi-hu and MO Jia-qi |
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| Institution: | Department of Electronics and Information Engineering, Bozhou Teachers College, Bozhou 236800, China and Department of Mathematic, Anhui Normal University, Wuhu 241003, China |
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| Abstract: | 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. |
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| Keywords: | fractional order differential equation singular perturbation asymptotic solution |
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