Abstract
This paper is concerned with the Navier–Stokes equations with time-fractional derivative of order α∈(0,1). This type of equations can be used to simulate anomalous diffusion in fractal media. We establish the existence and uniqueness of local and global mild solutions in Hβ,q. Meanwhile, we also give local mild solutions in Jq. Moreover, we prove the existence and regularity of classical solutions for such equations in Jq.