The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schr?dinger equation with Kerr nonlinearity and optical lattice.The approximate analytical soliton solutions are obtained based on the variational approach,which provides reasonable accuracy.Linear-stability analysis shows that all the solitons are linearly stable.No collapses are found when the Lévy index 1＜α≤2.For α=1,the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough.It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schr?dinger equation still holds in the one-dimensional fractional Schr?dinger equation.The physical mechanism for collapse prohibition is also given.