Predicting most likely application to be opened
How do you plan to predict the exact app?  Are you thinking of a user level model (you can't predict that a user will open app X if she doesn't have it installed in the first place) Or maybe you want to predict apps at a segment level( instead of predicting individual apps)
A neural network should work well if you have enough data since it has good "capacity"
The time series part comes from the fact that the probability of opening app depends on what app was opened before it. This is called "structured prediction" and is quite common in language models etc.
The output will be a distribution over the apps and you can use a soft max layer for the final output