一类非线性分数阶微分方程边值问题解的存在性  

Existence of Solutions for a Class of Nonlinear Riemann-Liouville Conformable Fractional Differential Equation

作　　者：黄娉娉 李媛[1] 彭钟琪 HUANG Ping-ping;LI Yuan;PENG Zhong-qi(School of Science,Shenyang University of Technology,Shenyang 110870,China)

机构地区：[1]沈阳工业大学理学院,辽宁沈阳110870

出　　处：《数学的实践与认识》2023年第1期257-265,共9页Mathematics in Practice and Theory

摘　　要：研究了一类带有Riemann-Liouville适型导数的非线性分数阶微分方程边值问题.利用Green函数的性质以及锥上不动点定理证明该边值问题正解的存在性.基于一个比较原则,利用单调迭代技巧以及上下解法证明该问题极值解的存在性.最后通过数值算例验证所得结论的有效性.In this paper,we study a class of boundary value problems for nonlinear fractional differential equations with Riemann-Liouville conformable derivatives.The existence of positive solutions of the boundary value problem is proved by using the properties of Green's function and fixed point theorem on cone.Based on a comparison principle,the existence of extremal solutions is proved by using the monotone iterative technique and the method of upper and lower solutions.Numerical examples are given to verify the validity of the methods.

关 键 词：Riemann-Liouville适型导数 不动点定理 分数阶微分方程 极值解 

分 类 号：O175.8[理学—数学]