一个分数阶微分方程两点边值问题解的存在唯一性  

The existence and uniqueness of the solution of a two-point boundary value problem for a fractional differential equation

作　　者：姜聪颖 侯成敏[1] JIANG Congying;HOU Chengmin(College of Science,Yanlian University,Yanji 133702,China)

机构地区：[1]延边大学理学院,延吉133002

出　　处：《黑龙江大学自然科学学报》2020年第6期638-643,共6页Journal of Natural Science of Heilongjiang University

基　　金：吉林省教育厅“十三五”科学技术研究项目(JJKH20170454KJ)。

摘　　要：针对带有两点边值条件的分数阶微分方程的解的存在性和唯一性问题,定义了适当的假设条件和合理的上下解,介绍了相关的比较原理。利用上下解方法和单调迭代方法,证明了线性问题解的存在性和唯一性,进而得到了所研究两点边值问题的微分方程的极端解,并证明了其解的存在性和唯一性,给出了一个例子验证了此结果。For the existence and uniqueness of the solutions of fractional differential equations with two-point boundary value conditions,appropriate assumptions and reasonable upper and lower solutions are defined,and the relevant comparison principles are introduced.The existence and uniqueness of the solution of the linear problem are proved by using the upper and lower solution method and the monotone iterative method,and then the extreme solution of the differential equation of the two-point boundary value problem is obtained,and the existence and uniqueness of the solution are proved.An example is given at the end to illustrate this result.

关 键 词：分数阶微分方程 上下解方法 单调迭代方法 存在性 唯一性 

分 类 号：O175.6[理学—数学]