There is no ambiguity regarding fasting for persons who are unable because of any sort of illness or during traveling. Allaah says in Qur’an;
“and whoever is ill or on a journey, the same number [of days which one did not observe Sawm (fasts) must be made up] from other days. Allaah intends for you ease, and He does not want to make things difficult for you. (He wants that you) must complete the same number (of days), and that you must magnify Allaah [i.e. to say Takbeer (Allaahu Akbar: Allaah is the Most Great)] for having guided you so that you may be grateful to Him” [al-Baqarah 2:185]
If a person is unable to fast because of illness or traveling. then he has to make up the fasts (after Eid and in the month of Shawwal) for the days (of illness and traveling), he has missed, when he becomes able to.
However, if there is no hope – according to doctors – that one may be cured and recovered from his sickness or that his illness worsens if he fasts, then he is exempted from fasting. As for compensation he has to pay ‘fidya’ or to feed one poor person for every day that he misses.
There is no such thing like ‘qasr’ (short) 'saum' (fast) for sick persons like ‘qasr’ (short) ‘salah’ (prayers) for travelers.