分数阶积分微分方程多点边值问题解的存在性和唯一性  

Existence and Uniqueness of Solutions of Multi-point Boundary Value Problems for Integro-differential Equations of Fractional Order

作　　者：窦丽霞[1] 刘锡平[1] 金京福[1] 王平友[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2012年第1期51-55,共5页Journal of University of Shanghai For Science and Technology

基　　金：上海市教委科研创新基金资助项目(10ZZ93);安徽省自然科学基金资助项目(10040606Q50)

摘　　要：研究一类非线性分数阶积分微分方程多点边值问题,通过计算边值问题的Green函数并分析Green函数的性质,利用压缩映射原理研究边值问题解的存在唯一性定理,并应用不动点定理得到了边值问题至少有一个解存在结论.同时给出了一个实例,说明所得结论.The existence and uniqueness of solutions were investigated for a class of multi-point boundary value problems of nonlinear integro-differential equations with fractional derivatives. Via calculating the Green＇s function and analyzing the properties of Green＇s function, the existence of solutions for multi-point boundary value problems was studied based on the Banach contraction, principle and by applying, the fixed point theorem. An example was given to illustrate the results.

关 键 词：分数导数 积分微分方程 多点边值问题 不动点定理 压缩映射原理 存在性和唯一性 

分 类 号：O075.1[理学]