In this paper, we establish a Lyapunov-type inequality for the half-linear local fractional ordinary differential equation based on the formulation of the local fractional derivative. In addition, we apply the inequality to investigate the non-existence and uniqueness of solutions for related homogeneous and non-homogeneous local fractional boundary value problems.

中文翻译：

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某些半线性局部分数常微分方程的Lyapunov型不等式

本文基于局部分数阶导数的表述，建立了半线性局部分数常微分方程的李雅普诺夫型不等式。此外，我们应用该不等式来研究相关齐次和非齐次局部分数边值问题解的不存在性和唯一性。