| 非线性分数阶微分方程三点边值问题解的存在性 |
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| 引用本文： | 韩仁基,蒋威.非线性分数阶微分方程三点边值问题解的存在性[J].数学研究,2011,44(2):128-138. |
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| 作者姓名： | 韩仁基 蒋威 |
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| 作者单位： | 1. 徽商职业学院基础部,安徽合肥,231201
2. 安徽大学数学科学学院,安徽合肥,230039 |
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| 基金项目： | supported by the National Nature Science Foundation of P.R. China(10771001); the Key Program of Ministry of Education of P.R.China(205068) |
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| 摘 要： | 讨论了一类非线性分数阶微分方程三点边值问题解的存在性.微分算子是Riemann-Liouville导算子并且非线性项依赖于低阶分数阶导数.通过将所考虑的问题转化为等价的Fredholm型积分方程,利用Schauder不动点定理获得该三点边值问题至少存在一个解.
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| 关 键 词： | 非线性分数阶微分方程 Riemann-Liouville分数阶导数 三点边值 Green函数 存在性 Schauder不动点定理 |
Existence of Solution for a Three-point Boundary Value Problem of Nonlinear Fractional Differential Equation |
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| Han Renji,Jiang Wei.Existence of Solution for a Three-point Boundary Value Problem of Nonlinear Fractional Differential Equation[J].Journal of Mathematical Study,2011,44(2):128-138. |
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| Authors: | Han Renji Jiang Wei |
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| Institution: | Han Renji~1 Jiang Wei~2 (1.Department of Basic Courses,Huishang Vocational College,Hefei Anhui 231201,2.School of Mathematical Sciences,Anhui University,Hefei Anhui 230039) |
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| Abstract: | In this paper,we discuss a three-point boundary value problem for a nonlinear differential equation of fractional order.The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order.We obtain the existence of at least one solution for integral equation using Schauder fixed-point theorem.Our analysis relies on the reduction of the problem considered considered to the equivalent Fredholm integral equation. |
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| Keywords: | Three-point boundary value problem Riemann-Liouville fractional derivative Existence Green's function Schauder fixed-point theorem |
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