What are the approved methods for calculating prayer times to create a reminder application?

It is good to do what reminds one of prayer. We do not have specialists in computational matters related to knowing how to calculate prayer times. One can use existing calendars and set the alarm time after the calendar time, as the calendar is an approximation and errors may sometimes occur with it, and prayer does not have to be performed at the very beginning of its time.

The calendar is a matter of ijtihad (independent reasoning), and prayer and fasting times should not be exclusively tied to it, because the beginning and end of these times are mentioned in the Qur'an and Sunnah. Therefore, reliance should be placed on what the legal texts indicate. Muezzins can benefit from these astronomical calendars as an approximation.