This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schauder fixed point theorem, we obtain the existence of solutions under the hypothesis that the nonlinear term satisfies the Carathéodory conditions. We apply the Banach contraction mapping principle to obtain the uniqueness of solutions. Moreover, by using the theory of spectral radius we prove the uniqueness and nonexistence of positive solutions. Finally, we illustrate our main results by some examples.

中文翻译：

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非线性项满足一些不等式的一类高阶分数阶边值问题解的存在和唯一性

本文关注于一类藏身级非线性分数阶边值问题。边界条件包含Riemann–Stieltjes积分和非局部多点边界条件。值得一提的是，非线性项和边界条件包含不同阶的分数导数。基于Schauder不动点定理，我们在非线性项满足Carathéodory条件的假设下获得了解的存在。我们应用Banach压缩映射原理来获得解的唯一性。此外，通过使用光谱半径理论，我们证明了正解的唯一性和不存在性。最后，我们通过一些例子说明我们的主要结果。