In this work, we investigate the condition of the given interval which ensures the existence and uniqueness of solutions for two-point boundary value problems within conformable-type local fractional derivative. The method of analysis is obtained by the principle of contraction mapping. Furthermore, benefiting from calculating the integral of the Green's function, we are able to improve a recent result by obtaining a sharper lower bound for an eigenvalue problem. Two examples are presented to clarify the obtained results. Finally, we present an open problem for the interested reader.

中文翻译：

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具有一致导数的两点分数边值问题唯一解的锐估计

在这项工作中，我们研究了给定区间的条件，该条件确保了一致型局部分数导数内两点边值问题解的存在性和唯一性。分析方法是根据收缩映射原理得到的。此外，受益于计算格林函数的积分，我们能够通过获得特征值问题的更清晰的下界来改进最近的结果。给出了两个例子来阐明所获得的结果。最后，我们向感兴趣的读者提出一个开放性问题。