  In this paper, we establish the existence of ground state solutions for a
fractional Schr\"odinger equation in the presence of a harmonic trapping
potential. We also address the orbital stability of standing waves.
Additionally, we provide interesting numerical results about the dynamics and
compare them with other types of Schr\"odinger equations. Our results explain
the effect of each term of the Schr\"odinger equation : The fractional power,
the power of the nonlinearity and the harmonic potential.
