一类分数阶三点边值问题解的存在性  

Existence of Solutions for a Class of Fractional Three-Point Boundary Value Problems

作　　者：李雯婧 

机构地区：[1]西北师范大学数学与统计学院,甘肃 兰州

出　　处：《理论数学》2021年第6期1048-1054,共7页Pure Mathematics

摘　　要：本文运用Leray-Schauder二择一定理,研究了一类分数阶微分方程的三点边值问题 得到该问题解的存在性。进一步证明了限制非线性项的函数k(t),在被形如Btμ的函数控制后,该问题至少存在一个解。最后,通过实例验证了结论的有效性。In this paper, three-point boundary value problem for a class of fractional differential equations are studied by using Leray-Schauder nonlinear alternative. The existence of the solution is obtained. Furthermore, it is proved that the function k(t), which is limited to the nonlinear term, exists at least one solution of the problem when it is controlled by a function of the form Btμ. Finally, an example is given to verify the validity of the conclusion.

关 键 词：分数阶微分方程 解的存在性 LERAY-SCHAUDER非线性抉择 GREEN函数 

分 类 号：O17[理学—数学]