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In this paper, we consider the fractional Navier-Stokes equations. We extenda previous non-uniqueness result due to Cheskidov and Luo, found in [5], fromNavier-Stokes to the fractional case, and from $L^1$-in-time,$W^{1,q}$-in-space solutions for every $q > 1$ to $L^s$-in-time,$W^{1,q}$-in-space solutions for appropriate ranges of $s,q$.

Density of weak solutions of the fractional Navier-Stokes equations in the smooth divergence-free vector fields