# Global existence for the nonlinear fractional Schr\"odinger equation with fractional dissipation

## TL;DR

This paper proves global existence and scattering results for the fractional nonlinear Schr"odinger equation with fractional dissipation, depending on the dissipation order.

## Contribution

It introduces new conditions under which solutions exist globally and scatter, considering the fractional dissipation effect.

## Key findings

- Global existence established for certain dissipation orders
- Scattering results proved depending on fractional dissipation
- Conditions identified for long-term behavior of solutions

## Abstract

We consider the initial value problem for the fractional nonlinear Schr\"odinger equation with a fractional dissipation. Global existence and scattering are proved depending on the order of the fractional dissipation.