| 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.分数阶微分方程边值问题解的存在性[J].应用泛函分析学报,2011,13(4):405-412. |
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| 作者姓名： | 周文学 |
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| 作者单位： | 兰州交通大学数学系,兰州730070;西安交通大学理学院,西安710049 |
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| 基金项目： | 国家自然科学基金，教育部科学技术研究重大项目 |
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| 摘 要： | 应用Gteen函数将分数阶微分方程边值问题可转化为等价的积分方程．近来此方法被应用于讨论非线性分数阶微分方程边值问题解的存在性．讨论非线性分数阶微分方程边值问题，应用Green函数，将其转化为等价的积分方程，并设非线性项满足Caratheodory条件，利用非紧性测度的性质和M6nch’s不动点定理证明解的存在性．
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| 关 键 词： | 边值问题 非紧性测度 Caratheodory条件 分数阶微分方程 Caputo分数阶导数 |
Existence of Solution to BVP for Fractional Differential Equation |
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| ZHOU Wenxue.Existence of Solution to BVP for Fractional Differential Equation[J].Acta Analysis Functionalis Applicata,2011,13(4):405-412. |
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| Authors: | ZHOU Wenxue |
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| Institution: | ZHOU Wenxue~(1,2) 1.Department of Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China 2.College of Sciences,Xi'an Jiaotong University,Xi'an 710049,China |
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| Abstract: | By the means of the Green's function,the boundary value problem of fractional differential equation can be reduced to the equivalent integral equation.Recently,this method is used successfully to discuss the existence of the solution to boundary value problem of nonlinear fractional differential equation.This article investigates the boundary value problem of nonlinear fractional differential equation.By applying Caratheodory conditions on the nonlinear terms,we obtain an existence result for solution.Our a... |
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| Keywords: | boundary value problem measure of noncompactness Caratheodory condition fractional differential equations Caputo fractional derivative |
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