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,2013,39(03):167-171.
一类高次分数阶微分方程正解的存在唯一性
- Title:
- Existence and uniqueness of the positive solution of a class of high-order fractional differential equation
- 文章编号:
- 1004-4353(2013)03-0167-05
- Keywords:
- Caputo derivative; Green function; mixed monotone operator
- 分类号:
- O175.8
- 文献标志码:
- A
- 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.
- 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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相似文献/References:
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GUO Cheng,DING Maosong,HAN Xiaoshuang*.Existence of positive solution for a fractional difference equations with fractional boundary value condition[J].Journal of Yanbian University,2015,41(03):25.
[2]祝相宇,孙明哲.一类分数阶差分方程正解的存在性[J].延边大学学报(自然科学版),2014,40(01):25.
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备注/Memo
收稿日期: 2013-04-17
作者简介: 杨慧(1976—),女,讲师,研究方向为泛函分析与微分方程.
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)