具非局部边界条件的奇异分数阶微分方程正解的存在性和唯一性
Existence and Uniqueness of Positive Solutions for Singular Fractional Differential Equation with Nonlocal Boundary Conditions
摘要: 本文研究了一类具非局部边界条件的奇异分数阶微分方程。先构造Green函数，并讨论相关性质，然后在一定条件下，借助Banach压缩映射原理和Krasnoselskii不动点定理，得到边值问题正解的存在性和唯一性。最后列举一个实例说明主要结果的可行性。
Abstract: In this paper, we mainly study a class of singular fractional order differential equations with nonlocal boundary conditions. Firstly, the properties of the Green function are discussed. Then, under some appropriate assumptions, by using the Banach contraction mapping principle and the Krasnoselskii Fixed Point theorem, the existence and uniqueness of positive solutions for the singular boundary value problems are obtained. An example is given to illustrate the feasibility of the main results.
文章引用：霍雪雪, 孙莉, 闫士浩, 周旋, 王广瓦. 具非局部边界条件的奇异分数阶微分方程正解的存在性和唯一性[J]. 理论数学, 2020, 10(3): 150-161. https://doi.org/10.12677/PM.2020.103022

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