| 一类高次分数阶微分方程正解的存在唯一性 |
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| 引用本文： | 杨慧,王文霞. 一类高次分数阶微分方程正解的存在唯一性[J]. 延边大学学报(自然科学版), 2013, 39(3): 167-171 |
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| 作者姓名： | 杨慧 王文霞 |
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| 作者单位： | 太原师范学院数学系,山西太原,030012 |
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| 基金项目： | 国家自然科学基金资助项目（11361047）;山西省高校科技开发项目（20111021）;山西省回国留学人员科研资助项目（2013-102）;青海省自然科学基金资助项目（2012-Z-910） |
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| 摘 要： | 研究Caputo型导数下的一类高次分数阶微分方程.首先给出等价于微分方程解的积分形式,然后利用格林函数的性质和混合单调算子不动点理论证明了这类分数阶微分方程正解的存在唯一性.
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| 关 键 词： | Caputo导数 Green函数 混合单调算子 |
Existence and uniqueness of the positive solution of a class of high-order fractional differential equation |
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| YANG Hui , WANG Wenxia. Existence and uniqueness of the positive solution of a class of high-order fractional differential equation[J]. Journal of Yanbian University (Natural Science), 2013, 39(3): 167-171 |
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| Authors: | YANG Hui WANG Wenxia |
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| Affiliation: | ( Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, China ) |
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| Abstract: | We study a class of high-order fractional differential equations involving Caputo fractional derivative. First we derive the integral form which is equivalent to the solution of differential equations, then existence and uniqueness theorem of the positive solution of the class of high-order fractional differential equation is given by using properties of the Green functions and the mixed monotone operator fixed point theory. |
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| Keywords: | Caputo derivative Green function mixed monotone operator |
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