This manuscript is dedicated to prove a new inequality that involves an important case of Leibniz rule regarding Riemann-Liouville and Caputo fractional derivatives of order $\alpha\in(0,1)$. In the context of partial differential equations, the aforesaid inequality allows us to address the Faedo-Galerkin method to study several kinds of partial differential equations with fractional derivative in the time variable; particularly, we apply these ideas to prove the existence and uniqueness of solution to the fractional version of the 2D Stokes equations in bounded domains.

中文翻译：

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关于莱布尼茨规则的分数形式

这份手稿致力于证明一个新的不等式，该不等式涉及莱布尼茨规则关于 $\alpha\in(0,1)$ 阶的 Riemann-Liouville 和 Caputo 分数阶导数的一个重要案例。在偏微分方程的背景下，上述不等式允许我们利用 Faedo-Galerkin 方法来研究几种在时间变量中具有分数阶导数的偏微分方程；特别是，我们应用这些想法来证明有界域中二维斯托克斯方程的分数版本的解的存在性和唯一性。