Is it permissible to rely on an inaccurate mobile application to know prayer times in the absence of the Athan (call to prayer) in expatriate countries?

The basic principle is that a Muslim should pray after verifying that the time for prayer has entered or having a strong presumption that it has. One should rely on calendars approved by trustworthy scholars, as long as they do not contradict the legal signs. As for unknown calendars, they can be used for approximation but should not be fully relied upon.