带有分数阶积分边值条件的分数阶微分方程的正解

Positive solutions of fractional differential equations with fractional integral boundary value conditions

讨论一类带有Riemann-Liouville型分数阶积分边值条件的分数阶微分方程边值问题,给出了该分数阶积分边值问题对应的Green函数及相关性质,并通过构造Banach空间上一个锥和对应的算子以及线性算子相关的第一特征值的讨论,运用不动点指数定理,得到该积分边值问题一个和两个正解的存在性.算例展示了定理的具体应用.

In this paper,a class of fractional-order boundary value problems with Riemann-Liouville type fractional integral boundary value conditions is discussed and the corresponding Green function and related properties of the fractional integral boundary value problem are given.By constructing a cone and corresponding operators in Banach space and discussing the first eigenvalue related to linear operators,using the fixed point index theorem,the existence of one and two positive solutions to the integral boundary value problem also obtained.Examples show the practical application of the theorem.