| 非线性项具有积分算子的分数阶反周期边值问题解的存在性与唯一性 |
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| 引用本文： | 刘华蓥,孙毅.非线性项具有积分算子的分数阶反周期边值问题解的存在性与唯一性[J].吉林大学学报(理学版),2015,53(5):835-840. |
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| 作者姓名： | 刘华蓥 孙毅 |
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| 作者单位： | 1. 东北石油大学 计算机与信息技术学院, 黑龙江 大庆 163318; 2. 吉林大学 数学学院, 长春 130012 |
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| 摘 要： | 考虑一个非线性项中含有关于未知函数的积分算子的非线性分数阶的反周期边值问题,其导数类型为Caputo型分数阶导数,阶数为2α≤3.应用Schauder不动点定理和压缩映象原理证明了该问题解的存在性与唯一性.
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| 关 键 词： | 分数阶微分方程 反周期边界条件 存在性 唯一性 |
| 收稿时间： | 2015-04-16 |
Existence and Uniqueness of Solution for a Fractional Anti-periodic Boundary Problem with Nonlinear Term Containing Integral Operators |
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| LIU Huaying,SUN Yi.Existence and Uniqueness of Solution for a Fractional Anti-periodic Boundary Problem with Nonlinear Term Containing Integral Operators[J].Journal of Jilin University: Sci Ed,2015,53(5):835-840. |
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| Authors: | LIU Huaying SUN Yi |
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| Institution: | 1. College of Computer and Information Technology, Northeast Petroleum University, Daqing 163318,Heilongjiang Province, China; 2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | A nonlinear fractional anti periodic boundary problem was considered, the differential operator of which is the Caputo sense of order 2<α≤3. The feature of this problem is that nonlinear term contains integral operators about unknownfunction. The existence and uniqueness of solution were proved via the Schauderfixed point theorem and the contraction mapping principle. |
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| Keywords: | fractional differential equation anti periodic boundary conditions existence uniqueness |
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