Mild solutions to the time fractional Navier–Stokes equations in RNRN

This paper addresses the existence and uniqueness of mild solutions to the Navier–Stokes equations with time fractional differential operator of order α∈(0,1)α∈(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 α  . Moreover, it is shown that the LpLp-exponent range, which the solution belongs to, is different from the range for the solution of the classical problem with α=1α=1.