I would like to have some evidence in deciding the safety of a prolonged use of the mobile on the eyes ( of course there is always the microwawe questions).
Yes, red-shifted light does not activate the cells in the retina that transduce time of day circadian information (ipRGCs), as they are sensitive to blue light. This means that night use of red shifted light on screens limits the amount of circadian disruption, which has a lot of health consequences. Reductions in short blue wavelengths are beneficial as well.
Some evidence:
Article Blue Blocker Glasses as a Countermeasure for Alerting Effect...
Screen apps that shift the display toward "yellower" or "redder" displays can be somewhat helpful, but it is also important, perhaps more important, to reduce the screen brightness as much as possible when using the display at night. See the study mentioned in the following story: