According to which time should a person traveling by plane break his fast?

The honorable Islamic law has made starting and breaking one's fast contingent upon discerning sunrise and sunset. God the Almighty says: “Eat and drink until the white thread of dawn becomes distinct from black. Then fast until nightfall” [2: 187].

It was recorded in the Sahih of Bukhari and the Sahih of Muslim that 'Umar Ibn Al-Khattab (may God be pleased with him) narrated that the Prophet (peace and blessings be upon him) said: “When night approaches from there and day retreats from there and the sun sets, then the person who is fasting has broken his fast," and that Abdullah Ibn Abu Awf (may God be pleased with him) said: "The Messenger of God said, 'If you see night approaching from there', and he pointed with his hand towards the east, 'then the person who is fasting has broken his fast.' " These hadiths prove that the decisive factor for breaking the fast is for the fasting person to physically discern nightfall by seeing it or by being informed of it by a trustworthy person and believing him. Likewise, what is important in starting the fast is for the person who is required to fast to ascertain the time of true dawn either by seeing it or being informed of it by a trustworthy individual.

It is known that as a person rises in elevation, sunset will be delayed and sunrise will be earlier with respect to him. This is the case for those who live on high floors due to the curvature of the earth. The legal principles then necessitate that a fasting person must not break his fast until the sun sets with respect to him. Imam Fakhr Al-Deen Al-Zaila'i, the Hanafi scholar, wrote in Tabyin Al-Haqa`iq Sharh Kanz Al-Daqa`iq: "It was reported that when the blind jurist Abu Musa, author of Al-Mukhtasar, went to Alexandria, he was asked about [the ruling for] someone who went up the Alexandria lighthouse and saw the sun long after it had set for those in the city, and whether it is permissible for him to break his fast." He said, "No, but it is permissible for those in the city [to break their fast] because each one is required to act according to what he has."

In his commentary, the luminary Ibn 'Abdin said: "It is stated in Al-Fayd that a person who is on an elevated place such as the lighthouse of Alexandria must not break his fast as long as the sun has not set for him; the residents of the city are to break their fast if the sun sets for them before it does for him. The same applies to the time of dawn concerning dawn prayers and the pre-dawn meal."
The ruling
The precept for breaking the fast for someone traveling by plane is by seeing the sun set at their location; passengers are not to break their fast according to the [local] time of the country over which they are flying, the country of their departure or the country of their destination. Rather, they must break their fast when they see that the whole disk of the sun has set.

However, if the period of fasting is prolonged to the extent that the durations become difficult for a person who is able to fast the usual hours, he may then break his fast due to the excessive hardship posed by travel but not because the fasting hours have ended; and he must make up the days on which he has broken his fast. Based on this, the in-flight announcements made by some pilots concerning breaking the fast according to the local time of the country of departure or the plane's current location are legally invalid.

A fasting person who is traveling by air must break his fast when the sun first sets. He is to ignore its subsequent appearances and disappearances which occur due to the speed of the airplane.

And God Almighty knows best.