Abstract
In this paper we use the tools from harmonic analysis to study the Cauchy problem for Navier-Stokes equations with time-fractional derivative of order a. (0, 1), which can be used to simulate the anomalous diffusion in fractal media. Two main results concerning the local existence of solutions for the given problem in Sobolev space are addressed. (C) 2017 Elsevier Ltd. All rights reserved.