非线性分数阶微分方程三点边值问题解的存在性(英文)  

Existence of Solution for a Three-point Boundary Value Problem of Nonlinear Fractional Differential Equation

作　　者：韩仁基[1] 蒋威[2] 

机构地区：[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

出　　处：《数学研究》2011年第2期128-138,共11页Journal of Mathematical Study

基　　金：supported by the National Nature Science Foundation of P.R. China(10771001);the Key Program of Ministry of Education of P.R.China(205068)

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.微分算于是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.In this paper, we discuss a three-point boundary value problem for a nonlinear differ- ential 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.

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 

分 类 号：O175.8[理学—数学]