This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.

中文翻译：

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具有多点积分边界条件的高阶非线性分数阶微分方程解的唯一性

本研究致力于开发具有积分和多点边界条件的高阶非线性分数阶微分方程的存在性和唯一性的替代条件。它使用基于积分算子的收缩迭代的不动点定理的新方法来解决相应的不动点问题。我们首先为在类似 b 度量的空间中具有收缩迭代的自映射开发存在唯一性定理。然后，我们通过利用适当的 b-metric-like 空间在合适的条件下获得问题的唯一可解性。