Yes, you can add different types of travel cards into FAIRTIQ.
Open the menu "Settings" > "Tickets" and add the card you own (such as a zone pass or a half-fare pass).
FAIRTIQ will bill your trips according to your travel cards. The system will not bill you for trips made within the subscription of your pass.
In case of ticket controls the valid travel card has to be presented to the control staff.
As of now, some travel cards such as the 9 O'Clock subscription (9-Uhr-Abo; available in some tariff community) or the Gleis 7 cannot be added to the app.