| 一类分数阶微分方程边值问题解的存在性 |
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| 引用本文： | 周文学,刘海忠.一类分数阶微分方程边值问题解的存在性[J].山东大学学报(理学版),2013,48(8):45-49. |
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| 作者姓名： | 周文学 刘海忠 |
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| 作者单位： | 1. 兰州交通大学数学系, 甘肃 兰州 730070; 2. 复旦大学数学科学学院, 上海 200433 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究了一类分数阶微分方程边值问题。 应用Green函数,将分数阶微分方程边值问题转化为等价的积分方程, 利用Schaefer不动点定理和Leray Schauder不动点定理得到了该边值问题存在解的充分条件, 推广和完善了已有的结果。
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| 关 键 词： | 边值问题 分数阶微分方程 Caputo型分数阶导数 不动点定理 |
| 收稿时间： | 2012-09-04 |
Existence of solution for the boundary value problem of a class of fractional differential equation |
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| ZHOU Wen-xue
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LIU Hai-zhong.Existence of solution for the boundary value problem of a class of fractional differential equation[J].Journal of Shandong University,2013,48(8):45-49. |
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| Authors: | ZHOU Wen-xue LIU Hai-zhong |
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| Institution: | 1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070， Gansu, China;
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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| Abstract: | A class of boundary value problem of fractional differential equation is studied. By the means of the Green′s function, the boundary value problem of fractional differential equation can be reduced to the equivalent integral equation, and some sufficient conditions on the existence of solution for the boundary value problem are obtained by using Schaefer′s fixed point theorem and Leray-Schauder fixed point theorem. Some known results are extended and improved. |
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| Keywords: | boundary value problem fractional differential equation Caputo fractional derivative fixed point theorem |
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