If you have a siddur or chumash on your phone and you drop it, do you kiss it if...
- the siddur is not open
- the siddur is open, but shem hashem is not showing
- the siddur is open and shem Hashem is showing
Thankfully, there are currently no smartphones that are made with e-paper.
Because of that, all smartphones today don't have the halachic status of writing, so you are allowed to switch screens from views which have Hashem's name on them, and it is not considered erasing the name. Even if they were made out of e-paper, I assume they would be given a halachic status of writing with sand, but the issue hasn't come up yet.
The reason we kiss books when they fall on the floor is out of respect to the book and the name which is in it. So while the name does not exist in written form in the phone, I can't see any harm with treating the phone with respect while the siddur app is open, or while you consider your phone a special place in which your siddur or Torah learning originates.