Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There are three times during which the Prophet prohibited us from praying or burying our deceased: sunrise until the sun has risen (some distance), when the sun is at its meridian, and when the sun is setting until it has completely set.
In his famous work, Fiqh As-Sunnah, Sheikh Sayyid Sabiq, elaborates on the subject as follows:
It is forbidden to pray after the Morning prayer until the sunrise and from the sunrise until the sun has completely risen to the length of a spear above the horizon, and when the sun is at its meridian until it moves sightly to the west, and after the Afternoon prayer until the sun sets.
Abu Sa`id reported that the Prophet (peace be upon him) said, “There is no prayer after the Morning prayer until the sun rises.” (Al-Bukhari and Muslim.)
`Amr ibn `Abbas related that he said, “O Prophet of Allah, inform me about the prayers.” He said, “Pray the Morning prayer and then abstain from prayer until sunrise and the sun has completely risen, for it rises between the horns of Satan. That is when the unbelievers prostrate to it. Then pray, as your prayer will be witnessed and attended to until the shadow of a spear becomes less than its length. At that time stop praying, for at that time the hell-fire is fed with fuel. When the shade comes, you may pray, for your prayer will be witnessed and attended (to by angels) until you pray the afternoon prayer. Then abstain from praying until the sun sets, for its sets between the horns of Satan, and that is when the unbelievers make prostrations to it.” (Ahmad and Muslim)
Said `Uqbah ibn `Amr, “There are three times during which the Prophet prohibited us from praying or burying our deceased: sunrise until the sun has risen (some distance), when the sun is at its meridian, and when the sun is setting until it has completely set.” (Related by “the group,” except for al-Bukhari)
Almighty Allah knows best.