非线性项具有积分算子的分数阶反周期边值问题解的存在性与唯一性  

Existence and Uniqueness of Solution for a Fractional Anti-periodic Boundary Problem with Nonlinear Term Containing Integral Operators

作　　者：刘华蓥[1] 孙毅[2] 

机构地区：[1]东北石油大学计算机与信息技术学院,黑龙江大庆163318 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2015年第5期835-840,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61170132);吉林省自然科学基金(批准号:201215038)

摘　　要：考虑一个非线性项中含有关于未知函数的积分算子的非线性分数阶的反周期边值问题,其导数类型为Caputo型分数阶导数,阶数为2<α≤3.应用Schauder不动点定理和压缩映象原理证明了该问题解的存在性与唯一性.A nonlinear fractional anti-periodic boundary problem was considered,the differential operator of which is the Caputo sense of order 2〈α≤3.The feature of this problem is that nonlinear term contains integral operators about unknown function.The existence and uniqueness of solution were proved via the Schauder fixed point theorem and the contraction mapping principle.

关 键 词：分数阶微分方程 反周期边界条件 存在性 唯一性 

分 类 号：O175.14[理学—数学]