一类具有Hadamard导数的分数阶微分方程积分边值问题正解的存在唯一性  

Existence and uniqueness of positive solutions of integral boundary value problems for a class of fractional differential equations with Hadamard derivatives

作　　者：胡芳芳 胡卫敏 张永 HU Fangfang;HU Weimin;ZHANG Yong(College of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China;Institute of Applied Mathematics,Yili Normal University,Yining 835000,Xinjiang,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《山东大学学报（理学版）》2024年第4期53-61,共9页Journal of Shandong University(Natural Science)

基　　金：伊犁师范大学校级资助项目(2023YSYB010);伊犁师范大学科研创新团队资助项目(CXZK2021016);伊犁州科技计划资助项目(YZ2022Y013)。

摘　　要：研究一类具有积分边值条件的Hadamard分数阶微分方程边值问题,利用Schauder不动点定理和上下解方法得到正解的存在性,通过Banach压缩映射原理得到唯一性结果,并给出实例说明结果的有效性。A class of boundary value problems for Hadamard fractional differential equations with integral boundary value conditions is studied.The existence of positive solutions is obtained by Schauder fixed point theorem and the upper and lower solution method.The uniqueness result is obtained by Banach compression mapping principle,and an example is given to illustrate the effectiveness of theresults.

关 键 词：Hadamard分数阶导数 分数阶微分方程 不动点定理 存在唯一性 

分 类 号：O175.14[理学—数学]