In this paper, we work on a general comparison principle for Caputo fractional-order ordinary differential equations. A full result on maximal solutions to Caputo fractional-order systems is given by using continuation of solutions and a newly proven formula of Caputo fractional derivatives. Based on this result and the formula, we prove a general fractional comparison principle under very weak conditions, in which only the Caputo fractional derivative is involved. This work makes up deficiencies of existing results.

中文翻译：

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Caputo分数阶常微分方程的一般比较原理

在本文中，我们研究了 Caputo 分数阶常微分方程的一般比较原理。通过使用解的延续和新证明的 Caputo 分数阶导数公式，给出了 Caputo 分数阶系统的最大解的完整结果。基于这个结果和公式，我们证明了一个在非常弱的条件下的一般分数比较原理，其中只涉及 Caputo 分数导数。这项工作弥补了现有成果的不足。