All perfect praise be to Allah, The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
Booking an airline ticket goes under Forward Ijarah (Hiring) because the required benefit (Carrying a passenger to a certain destination) should be provided by the hirer. Moreover, it was called as such because the benefit is expected from the hirer, and not from what`s hired out. Therefore, that benefit has to be governed by certain specifications which distinguish it from other benefits. Muslim jurists are of the view that Forward Ijarah is permissible. However, they disagreed about the rent being paid in the same sitting.
Although there is a variety of views in this regard, it was agreed on two of them:
First: Shafie scholars said: "In order for the Forward Ijarah to be valid, the hirer should collect the rent in the same sitting. If the contracting parties left before payment is made, this Ijarah is rendered invalid." {Moghni al-Mohtaj by al-Shirbini, vol./pp.451-452}.
Second: Hanfie scholars said that it is permissible to delay payment of rent in all types of Ijarah. Hanbalie scholars share this view, but they conditioned that the Forward Ijarah isn`t conducted in the manner of a Salam (Buying in advance). We (Iftaa` Dept.) opt for the opinion of the Hanbalie scholars, which doesn`t stipulate paying in advance, in order to facilitate for people. This is also the view of some Shafie scholars as mentioned in [Al-Bayan, vol.7/pp.339] by Al-Imrani.
In conclusion, it is permissible for the person who can`t afford to buy tickets in cash to pay in installments as long as the purpose of hisjourney is lawful, such as obtaining a degree and the like. And Allah Knows Best.