具有奇异项的分数阶微分方程边值问题  

Boundary Value Problems of Fractional Differential Equations with Singular Terms

作　　者：张玲玲 张楠 ZHANG Lingling;ZHANG Nan(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《山西大学学报（自然科学版）》2022年第3期511-519,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省重点研发计划项目(国际科技合作)(201903D421042);山西省回国留学人员科研资助项目(2021-030)。

摘　　要：文章研究了一类具有奇异项的Caputo型分数阶微分方程边值问题。首先利用非线性算子理论及相关性质给出了算子方程A(x,x)=x存在唯一解的条件,由此获得了该边值问题存在唯一解的若干充分条件。最后,通过应用举例,对主要结果做了进一步验证。In this paper,we study the boundary value problems for a class of Caputo fractional differential equations with singular terms.Firstly,the conditions for the existence and uniqueness of solution to the operator equation A(x,x)= x are given by using the nonlinear operator theory and related properties,and then some sufficient conditions for the existence and uniqueness of solution to the boundary value problems are obtained.Finally,as an application example,the main results are further verified.

关 键 词：分数阶微分方程 混合单调算子 奇异项 解的存在唯一性 

分 类 号：O175[理学—数学]