The Lajnah Daa’imah stated:

“If the sick person finds hardship in offering each Salah at its due time, they can combine the Zhuhr (Noon) Prayer with the `Asr (Afternoon) Prayer, and Maghrib (Sunset) Prayer with `Isha’ (Night) Prayer at the time of the earlier or later one, according to their circumstances and ability.” [Reference but not available due to website construction]

Note: As for shortening the prayer, then the sick person is not allowed to shorten his or her prayers except in a state of traveling and Allaah knows best.

Mentioned by

AbdulFattaah Bin Uthman
Abu Fajr