%0 Journal Article
%T 一类分数阶三点边值问题解的存在性<br>Existence of Solutions for a Class of Fractional Three-Point Boundary Value Problems
%A 李雯婧
%J Pure Mathematics
%P 1048-1054
%@ 2160-7605
%D 2021
%I Hans Publishing
%R 10.12677/PM.2021.116118
%X <div style=\"text-align:justify;\">
	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<img src=\"Edit_2fa48dc3-b926-4020-aa61-86f752e84e6a.png\" alt=\"\" /> 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Bt<sup>μ</sup>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。<br />
In this paper, three-point boundary value problem for a class of fractional differential equations <img src=\"Edit_8a6452e7-a590-47e3-8ecc-189f9c54b567.png\" alt=\"\" /> 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 Bt<sup>μ</sup>. Finally, an example is given to verify the validity of the conclusion.
</div>
%K 分数阶微分方程，解的存在性，Leray-Schauder非线性抉择，Green函数<br>Fractional Differential Equation
%K Existence of Positive Solutions
%K Leray-Schauder Nonlinear Alternative
%K Green Function
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=43066