无穷区间上分数阶微分方程积分边值问题  

Integral Boundary Value Problems of FractionalDifferential Equations on Infinite Interval

作　　者：李悦 刘锡平[1] LI Yue;LIU Xiping(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《吉林大学学报（理学版）》2023年第4期761-771,共11页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11171220).

摘　　要：考虑一类具有多个分数阶导数项的Riemann-Liouville型分数阶微分方程在无穷区间上的积分边值问题.通过构造新的Banach空间,利用非线性分析理论,在非线性项满足L 1-Carathéodory条件的情况下,得到了边值问题正解存在及唯一的多个结论,并给出实例说明所得结果的适用性和通用性.We considered integral boundary value problem of a class of Riemann-Liouville fractional differential equations with multiple fractional derivative terms on infinite intervals.By constructing a new Banach space and using the nonlinear analysis theory,and under the condition that the nonlinear term satisfied the L 1-Carthéodory conditions,some conclusions for existence and uniqueness of positive solutions to boundary value problems were obtained,and an example was used to illustrate the applicability and universality of the obtained results.

关 键 词：分数阶微分方程 无穷区间 积分边值问题 L 1-Carathéodory条件 不动点定理 

分 类 号：O175.8[理学—数学]