Is prayer obligatory according to the prayer times of the city where the Muslim resides, or according to his feelings or the muezzin's apps on the mobile phone, and what is the method for calculating prayer times in Turkey?

If the prayer time can be ascertained by the Shar'i signs, then performing the prayer and commencing the fast (imsak) based on them becomes obligatory. If the Shar'i signs cannot be ascertained, then it is obligatory to pray after certainty or strong presumption that the time has begun, and it is not valid with doubt. As for commencing the fast (imsak), it is permissible to eat until certainty or strong presumption that the time has begun. Reliable calendars, approved by trustworthy scholars, are to be acted upon unless they contradict the Shar'i signs. As for unknown calendars, they may be used for approximation but not relied upon entirely.