Update 11/27: An update of the App was just pushed out on iOS which now includes the south side stations, including Providence.
Apparently, Wickford Junction is not yet included. MBTA says it will be added in the next update.
The MBTA’s new mobile Commuter Rail ticketing app, mTicket, launched today, but only on Commuter Rail lines out of North Station.
We can expect the mTicket system to be available for trips on the Providence line starting later this month, and monthly passes for December will also be able to be purchased using mTicket. The MBTA has an FAQ to answer any questions about the system.