I have an application that runs on an embedded Linux device and every now and then changes are made to the software and occasionally also to the root file system or even the ins
Currently, there are quite a few Open Source embedded Linux update tools growing, with different focus each.
Another one that is worth being mentioned is RAUC, which focuses on handling safe and atomic installations of signed update bundles on your target while being really flexible in the way you adapt it to your application and environment. The sources are on GitHub: https://github.com/rauc/rauc
In general, a good overview and comparison of current update solutions you might find on the Yocto Project Wiki page about system updates:
https://wiki.yoctoproject.org/wiki/System_Update