How are prayers performed in places where prayer times do not occur?

Time is one of the conditions for prayer. While some Islamic scholars, based on the reasoning that "time is a condition for prayer," have stated that the obligatory prayer is not required in places where the prayer times do not occur, the majority of scholars, considering that the true cause of prayer is the divine command, have ruled that in such regions, prayers should be performed by estimation. (Ibn Abidin, Radd al-Muhtar, 1/362) In a narration, the Prophet (peace be upon him) stated that in the end times, when the Dajjal appears, a day will be like a year, a day will be like a month, and a day will be like a week, and that during these days, prayers should be performed by estimation (Muslim, Fitan, 110 [2937]). This narration is one of the evidences for this view. This hadith shows that the absence of prayer times does not remove the obligation of prayer, and clearly indicates that in regions and times where prayer times do not occur, prayers should be performed by estimating the times. It is understood that, due to the divine command, the Sunnah of the Prophet (peace be upon him), and practical consensus, all Muslims are obligated to perform five daily prayers within a 24-hour period. Otherwise, Muslims living in certain parts of the world, such as the poles or regions near the poles (where there are six months of day and six months of night), would only perform five prayers in a whole year. Therefore, if the time for a particular prayer does not occur or cannot be precisely determined in a region, that prayer should be performed by estimating its time.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu