For me, the premiere example of fasting in the Bible is Christ’s fast in the desert. He also discussed it with the apostles, as being the only way some devils can be driven out.
So, perhaps we have little or nothing more to discuss.
Second, when his disciples asked him why they couldn't cast out that particular demon, he specified 'this kind' - a dumb and deaf spirit. Do you have a Bible version that adds 'a gluttony spirit' to that description?
Mark 9:29 - And he said unto them, This kind can come forth by nothing, but by prayer and fasting.