| 一类含积分边界条件分数阶微分方程解的存在性和唯一性 |
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| 引用本文： | 薛益民,苏莹,苏有慧.一类含积分边界条件分数阶微分方程解的存在性和唯一性[J].安徽师范大学学报(自然科学版),2017,40(4). |
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| 作者姓名： | 薛益民 苏莹 苏有慧 |
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| 作者单位： | 徐州工程学院数学与物理科学学院,江苏徐州,221018;徐州工程学院数学与物理科学学院,江苏徐州,221018;徐州工程学院数学与物理科学学院,江苏徐州,221018 |
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| 基金项目： | 国家自然科学基金,国家自然科学数学天元基金,江苏省自然科学基金,江苏省高校自然科学基金,江苏省六大人才高峰项目,安徽省教育厅重点项目 |
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| 摘 要： | 研究一类含积分边界条件非线性分数阶微分方程{~CD~αu(t)+f(t,u(t))=0,2α3,0t1, u(0)=u″(0)=0,u(1)=λ∫10u(s)ds,0λ2,解的存在性和唯一性,借助于Green函数的性质,利用Schauder不动点定理和Banach压缩映射原理,得到该边值问题解的存在性和唯一性定理,并举例验证所得结论的有效性.
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| 关 键 词： | 分数阶微分方程 积分边值条件 不动点定理 Green函数 |
Existence and Uniqueness of Solutions for a Fractional Differential Equations with Integral Boundary Value Conditions |
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| XUE Yi-min,SU Ying,SU You-hui.Existence and Uniqueness of Solutions for a Fractional Differential Equations with Integral Boundary Value Conditions[J].Journal of Anhui Normal University(Natural Science Edition),2017,40(4). |
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| Authors: | XUE Yi-min SU Ying SU You-hui |
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| Abstract: | In this paper,we studied the following nonlinear fractional differential equations with integral boundary value conditions as the form of { CDαu(t) + f(t,u(t)) =0,2 ＜ α ＜ 3,0 ＜ t ＜ 1,u(0) u"(0) =0,u(1) =λ∫10 u(s)ds,0 ＜ λ ＜ 2,The theorems of the existence and uniqueness were obtained by using the properties of the associated Green's function Schauder,fixed point theorem and banach contraction mapping principle.Three examples were given to illustrate the advantages of the obtained results. |
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| Keywords: | fractional differential equations integral boundary conditions fixed point theorem Green function |
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