| 一类分数阶非线性时滞问题的奇摄动 |
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| 引用本文： | 朱红宝. 一类分数阶非线性时滞问题的奇摄动[J]. 应用数学和力学, 2019, 40(12): 1356-1363. DOI: 10.21656/1000-0887.400195 |
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| 作者姓名： | 朱红宝 |
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| 作者单位： | 安徽工业大学 数理科学与工程学院, 安徽 马鞍山 243002 |
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| 基金项目： | 安徽省高校自然科学研究重点项目(KJ2019A0062) |
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| 摘 要： | 讨论了一类奇异摄动非线性分数阶时滞问题.首先利用奇异摄动方法求出了问题的外部解.再利用伸展变量法构造了问题在边界附近的两个边界层校正项，得出了所提问题的形式渐近解.最后，在合适的假设条件下，利用微分不等式理论证明了解的一致有效性，并给出了结论及未来的研究方向.
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| 关 键 词： | 分数阶微分方程 非线性 时滞 奇摄动 |
| 收稿时间： | 2019-06-20 |
A Class of Fractional Nonlinear Singularly Perturbed Problems With Time Delays |
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| Affiliation: | School of Mathematics & Physics, Anhui University of Technology, Maanshan, Anhui 243002, P.R.China |
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| Abstract: | A class of fractional nonlinear singularly perturbed problems with time delays were considered. Firstly, the outer solution was constructed by means of the singular perturbation method. Then, a stretched variable was introduced to obtain 2 boundary layer correction items for the solution, and the asymptotic analytic expansion solution to the problem was also acquired. Finally, under suitable conditions, the theory of differential inequalities was applied to prove the uniformly valid asymptotic expansion of the solution to the original problem, and the conclusion with the future research directions was given. |
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