In this article, based on further investigation of the properties of the Green function, together with a fixed point theorem due to Avery-Peterson, height functions on special bounded sets are constructed to obtain the existence of triple positive solutions for higher-order fractional integral boundary value problems. The nonlinearity permits singularities both on the time and the space variables.

中文翻译：

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空间变量上具有奇异性的高阶分数积分边值问题的多重正解

本文在进一步研究格林函数性质的基础上，结合 Avery-Peterson 的不动点定理，构造特殊有界集上的高度函数，以获得高阶分数积分的三正解的存在性。边值问题。非线性允许时间和空间变量的奇异性。