  We apply a composite idea of semi-discrete finite difference approximation in
time and Galerkin finite element method in space to solve the Navier-Stokes
equations with Caputo derivative of order 0 < {\alpha} < 1. The stability
properties and convergence error estimates for both the semi-discrete and fully
discrete schemes are obtained. Numerical example is provided to illustrate the
validity of theoretical results.

Numerical Analysis