Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper addresses the existence and uniqueness of mild solutions to the Navier-Stokes equations with time fractional differential operator of order alpha is an element of (0, 1). Several interesting properties about the solution are also highlighted, like regularity and decay rate in Lebesgue spaces, which will depend on the fractional exponent alpha. Moreover, it is shown that the L-P-exponent range, which the solution belongs to, is different from the range for the solution of the classical problem with alpha = 1. (C) 2015 Elsevier Inc. All rights reserved.2597 29482980Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2013/00594-8]CNPq [302865/2012-8]