Musannaf Ibn Abi Shaybah

Hazrat Aisha (may Allah be pleased with her) narrates that the Noble Prophet (peace and blessings be upon him) would sometimes perform shortened prayers during travel and sometimes complete, sometimes he would fast and sometimes not fast, he would delay the Zuhr prayer and offer Asr early, he would delay Maghrib and offer Isha early.

Hazrat Abu Qilabah says that if you perform two rak'ahs during travel, this is also Sunnah, and if you perform four, this is also Sunnah.

Hazrat Aisha (may Allah be pleased with her) used to perform the full prayer while traveling.

Hazrat Anu Najeeh Makki says that the companions of the Holy Prophet (peace and blessings be upon him) used to travel together; some would perform the full prayer and some would shorten it, some would fast and some would not fast. Despite this, no one would criticize another.

Hazrat Bustam bin Muslim says that I asked Hazrat Ata about shortening the prayer during travel, so he replied that if you shorten it, it is a concession, and if you wish, you may offer the full prayer.

Hazrat Maymun bin Mehran asked Hazrat Saeed bin Musayyib about prayer during travel, so he replied: If you wish, perform two rak'ahs, and if you wish, perform four rak'ahs.