First of all, we would like to stress that Muslims are required to perform daily prayers at their appointed times. However, Muslims living in high latitudes may face several problems regarding the timing of their fasting and prayer. Muslim scholars have discussed this problem and presented detailed solutions for it.
Regarding this issue, the European Council for Fatwa and Research has stated the following:

The council discussed the topic of the times (Mawaqit) for Prayers and fasting in countries that are located at high latitudes and listened to the Shar`i and astronomical studies that were submitted by some of the members, and the illustrations of the relevant technical aspects recommended in the Eleventh Session of the Council, and decided the following:
First: Confirming the Sixth Resolution taken by the Muslim World League’s Islamic Fiqh Academy concerning the times for Prayers and fasting in the countries located at high latitudes.

Following is its text:
Praise is due to Allah Alone, and peace and blessings upon His Messenger Muhammad.
In its Ninth Session held at the building of the Muslim World League, Makkah Al-Mukarramah during the period from Saturday, Rajab 12, 1406 to Saturday, Rajab 19, 1406, the Council of the Islamic Fiqh Academy looked into the topic of the times for Prayers and fasting for those who live in the regions at high latitudes.
In agreement with the spirit of the sharia that is based on leniency and the elimination of inconvenience, and according to the report of the Committee of Astronomical Experts, the Council took the following decision on the subject:
1. In order to remove the disorder resulting from multiple ways of calculation, there shall be determined for each Prayer time for the astronomical signs that agree with what the sharia has indicated and with what the scholars of Shar`imiqat have shown regarding changing these signs to astronomical calculations related to the position of the sun above or below the horizon, as follows:

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A. Fajr: It correlates with the appearance of the first white light and it spreads across the horizon “true dawn,” and this corresponds to the angle 18 degrees below the eastern horizon.
B.Shuruq (sunrise): It correlates with the emergence of the upper edge of the solar disc from under the eastern horizon and it is estimated at an angle of 50 minutes under the horizon.
C. Zhuhr: It correlates with the passage of the sun across the meridian that represents the highest daily position of the sun corresponding to the shortest shadow cast by standing objects.
D.`Asr: It correlates with the position of the sun when the shadow of an object becomes equal to its length plus the minimum length of the shadow of midday. The angle of this position varies with the variation of time and place.
E. Maghrib: It correlates with the complete disappearance of the solar disc below the western horizon. Its angle is estimated at 50 minutes below the horizon.
F.`Isha’: It corresponds with the disappearance of the red twilight when the sun is situated at 17 degrees below the western horizon.

2. When determining the times it is enough to add two minutes of time to the times of Zhuhr, `Asr, Maghrib and `Isha’, and to subtract two minutes of time from the times of Fajr and shuruq.
3.The regions at high latitudes are divided into three zones:

A. The first zone: It is the region that lies between the latitudes of 45 degrees and 48 degrees north and south. It is characterized by the existence of the apparent signs of the time during twenty-four hours, no matter whether the times are long or short.
B. The second zone: It lies between the latitudes of 48 degrees and 66 degrees north and south, where some of the astronomical signs of time are nonexistent for a number of days during the year, as, for example, the case when the twilight does not disappear to indicate the beginning of `Isha’, and thus the end of the Maghrib time trails till it overlaps Fajr.
C. The third zone: It lies at the latitude of 66 degrees north and south and extends to the two poles. In this zone the apparent signs indicating the time are nonexistent for a long period of the year both by day and at night.

4. The ruling for the first zone is that its people observe the Prayers at their Shar`i times, and observe fasting for its Shar`i time, from true dawn till sunset, in compliance with the Shar`i texts indicating the times for Prayers and fasting; and if someone is unable to fast or complete his fast on a certain day because of its excessive length, he or she may break his or her fast on that day and compensate for it on some other suitable day.
5. The ruling for the second zone is that the times for `Isha’ and Fajr Prayers are to be determined with the proportional measurement on the analogy of the corresponding times in the night of the closest region where the signs of the times of `Isha’ and Fajr can be distinguished. The Council of the Academy suggests the latitude of 45 degrees as the closest region where worshiping or recognition is comfortably possible. If `Isha’ begins after the third part of the night at 45 degrees latitude, `Isha’ will start similarly in respect to the night at the place where the time is to be determined [i.e., after the third part of the night], and the same is true regarding Fajr.
6. The ruling for the third zone is that all the times are calculated with the proportional measurement in analogy of the corresponding times at 45 degrees latitude, by dividing the 24 hours in the third zone in the same way the times are divided at 45 degrees latitude.
If the length of the night at 45 degrees latitude is 8 hours and the sun sets at 8 o’clock, and `Isha’ is at 11 o’clock, the same times will be observed in the country where the time is to be determined. If the time of Fajr at 45 degrees latitude is 2 a.m., Fajr in the country where the time is to be determined will be at 2 a.m. and fasting will begin at that time and continue up to the estimated time of Maghrib.

All this is on the analogy of the estimation mentioned in the hadith about the antichrist where we read: “We said, ‘O Allah’s Messenger! How long will he (the antichrist) live on earth?’ He said, ‘Forty days: one day as long as a year, and one day as long as a month, and one day as long as a week.’ We said, ‘O Allah’s Messenger! During the day that will be as long as a year, will it be sufficient for us to perform only the Prayers of one day and night?’ He said, ‘No. But estimate (the Prayer times) for it’” (Muslim and Abu Dawud).

Allah is the source of all success, and peace and blessings upon Prophet Muhammad and his family and Companions. (End of the Resolution of the Fiqh Academy.)

Second: Since this issue is a matter of ijtihad, due to there being no definitive final texts pertaining to it, the Council does not find any harm in depending on other estimations made by other Islamic committees of fatwa, such as resorting to the solar depression of 12 degrees corresponding to the Fajr and `Isha’ Prayers, and the fixing of the time interval between the times of Maghrib and `Isha’, on the one hand, and the time of Fajr and sunrise, on the other hand, as one-and-a-half hours.

The Council advises Islamic bodies in charge of mosques and Islamic centers to follow the method suggested by the Council that agrees with the conclusions arrived at by the Islamic Fiqh Academy in Makkah Al-Mukarramah, as mentioned above.

Third: The Council confirms its previous Decision No. 3/3 concerning the legitimacy of performing the Maghrib and `Isha’ Prayers together on missing the sign of `Isha’ or the delay of its time, in order to save the Muslims living in high latitudes inconvenience and difficulty.