Objection 1. It would seem that fasting is not an act of abstinence. For Jerome [The quotation is from the Ordinary Gloss, where the reference is lacking] commenting on Matthew 17:20, "This kind of devil" says: "To fast is to abstain not only from food but also from all manner of lusts." Now this belongs to every virtue. Therefore fasting is not exclusively an act of abstinence.
Objection 2. Further, Gregory says in a Lenten Homily (xvi in Evang.) that "the Lenten fast is a tithe of the whole year." Now paying tithes is an act of religion, as stated above (Question 87, Article 1). Therefore fasting is an act of religion and not of abstinence.
Objection 3. Further, abstinence is a part of temperance, as stated above (Q143,146, 1, ad 3). Now temperance is condivided with fortitude, to which it belongs to endure hardships, and this seems very applicable to fasting. Therefore fasting is not an act of abstinence.
On the contrary, Isidore says (Etym. vi, 19) that "fasting is frugality of fare and abstinence from food."
I answer that, Habit and act have the same matter. Wherefore every virtuous act about some particular matter belongs to the virtue that appoints the mean in that matter. Now fasting is concerned with food, wherein the mean is appointed by abstinence. Wherefore it is evident that fasting is an act of abstinence.
Reply to Objection 1. Properly speaking fasting consists in abstaining from food, but speaking metaphorically it denotes abstinence from anything harmful, and such especially is sin.
We may also reply that even properly speaking fasting is abstinence from all manner of lust, since, as stated above (1, ad 1), an act ceases to be virtuous by the conjunction of any vice.
Reply to Objection 2. Nothing prevents the act of one virtue belonging to another virtue, in so far as it is directed to the end of that virtue, as explained above (32, 1, ad 2; 85, 3). Accordingly there is no reason why fasting should not be an act of religion, or of chastity, or of any other virtue.
Reply to Objection 3. It belongs to fortitude as a special virtue, to endure, not any kind of hardship, but only those connected with the danger of death. To endure hardships resulting from privation of pleasure of touch, belongs to temperance and its parts: and such are the hardships of fasting.
Source: Summa Theologica (New Advent)