含积分边界条件的分数阶微分方程边值问题的正解的存在性

摘要

研究了含积分边界条件的分数阶微分方程的边值问题，首先给出格林函数及性质，其次将问题转化为一个等价的积分方程，最后应用 Krasnoselkii 及 Leggett-Williams不动点定理得到了一个及多个正解的存在性，推广了以往的结果。%In this paper, we consider the existence of positive solutions for fractional boundary value problems with integral boundary conditions. First, we give the properties of Green′s function. Second, the problem has been reduced to the equivalent Fredholm integral equation. Finally, using Krasnoselkii fixed point theorem and Leggett-Williams fixed point theorem, some results on the existence of positive solutions are obtained. The work is an extension of the previous results.