  Discrete nonlinear Schrodinger equation (DNLS) describes a chain of
oscillators with nearest neighbor interactions and a specific nonlinear term.
We consider its modification with long-range interaction through a potential
proportional to $1/l^{1+\alpha}$ with fractional $\alpha < 2$ and $l$ as a
distance between oscillators. This model is called $\alpha$DNLS. It exhibits
competition between the nonlinearity and a level of correlation between
interacting far-distanced oscillators, that is defined by the value of
$\alpha$. We consider transition to chaos in this system as a function of
$\alpha$ and nonlinearity. It is shown that decreasing of $\alpha$ with respect
to nonlinearity stabilize the system. Connection of the model to the fractional
genezalization of the NLS (called FNLS) in the long-wave approximation is also
discussed and some of the results obtained for $\alpha$DNLS can be
correspondingly extended to the FNLS.
