  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.
