  In this work, we consider time-fractional Navier-Stokes equations (NSE) with
the external forces involving finite delay. Equations are considered on a
bounded domain in 3-D space having sufficiently smooth boundary. We transform
the system of equations (NSE) to an abstract Cauchy problem and then
investigate local existence and uniqueness of the mild solutions. In
particular, with some suitable condition on initial datum we establish the
global continuation and regularity of the mild solutions. We use semigroup
theory, tools of fractional calculus and Banach contraction mapping principle
to establish our results.
