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In this work, we consider time-fractional Navier-Stokes equations (NSE) withthe external forces involving finite delay. Equations are considered on abounded domain in 3-D space having sufficiently smooth boundary. We transformthe system of equations (NSE) to an abstract Cauchy problem and theninvestigate local existence and uniqueness of the mild solutions. Inparticular, with some suitable condition on initial datum we establish theglobal continuation and regularity of the mild solutions. We use semigrouptheory, tools of fractional calculus and Banach contraction mapping principleto establish our results.

Mild solutions of time fractional Navier-Stokes equations driven by finite delayed external forces