Reference: Fataawa Muhimmah tata’allaq bis-Salaah – Question 1, Page 3
Question: In some places [on Earth], the night or the day continue for a long [period of] time, and [in others] they are so short that the time is insufficient for the five [obligatory] prayers; so how should the residents there pray?
Response: It is incumbent upon the residents in these places where the day or night extend [for long periods] to pray their five [daily] prayers by estimating, if they do not have a zawaal or sunset during a 24-hour period. Just as has authentically been reported from the Prophet (sal-Allaahu ‘alayhi wa sallam) in the hadeeth of Nawwaas ibn Sam’aan as transmitted in Saheeh Muslim about the first day [when] Dajjaal [will appear] being as [long as] a year, [and] the companions asked the Messenger of Allaah (sal-Allaahu ‘alayhi wa sallam) about [the obligatory prayers on] that [day], and he said:
And similarly will be [the case] on the second day of the days of Dajjaal [presence] which will be as [long as] a month, and similarly the day which is as [long as] a week.
As for the place where during a 24-hour period the night is short and the day is long, or vice versa, then its ruling is clear – they are to pray during it like all the other days, even if the night or day are very short; and this is based upon the generality of [all] the [authentic] evidences.
And Allaah is the Expounder of [all] success.