Rather, it is something that should involve our body parts in terms of leaving off different sins. Our tongues should fast from all forms of evil speech. Our hearing should fast from listening to evil speech and all of those other things that Allah is not pleased with. Even our eyesight should refrain from looking at those things that Allah is displeased with.
"All the deeds of Adam's descendants are for themselves, with each good deed rewarded tenfold to 700 times its worth – except for fasting, since it is for Me, and I will reward it. He leaves off his desires, his food, and his drink for My sake. As well, he that fasts has two moments of joy: one at the time of breaking his fast, and the other at the time when he will meet his Lord; and indeed, the smell of the mouth of the fasting person is better with Allah (SWT) than the smell of musk." - [Al-Bukhari and Muslim]