There are many options in the market and in the community about virtual desktop and remote control, but until now I haven't seen any solution to be able to just control the smartphone (android) just using the computer mouse under the linux, as if it were a second monitor, but each screen operating your operational system.

If there's any way to do this in Linux, for those who need to keep this constant flow between Desktop and Mobile, it would be a perfect solution to just leave the phone aside and control it as if it were an external monitor (without needing to mirror the image on the monitor, because the phone will be already positioned on the side)