"And he said unto them, This kind can come forth by nothing, but by prayer and fasting." Mark 9:29
Prayer and fasting do not drive certain demons out. If the name of Jesus and faith in His name won't do the job, then fasting and prayer won't either. Jesus is saying that fasting and prayer are the only ways of casting out this type of unbelief.
An unbelief that comes as a result of ignorance can be done away with by receiving the truth of God's Word (Rom. 10:17; 2 Pet. 1:4). However, the unbelief that hindered the disciples in this case was a "natural" type of unbelief. They had been taught all of their lives to believe what their five senses told them. They were simply dominated by this natural input more than by God's supernatural input (God's Word). The only way to overcome this unbelief that comes through our senses is to deny our senses through prayer and fasting.
Fasting accomplishes many things. One of the greatest benefits of fasting is that through denying the lusts of the flesh, the spirit man gains ascendancy. Fasting was always used as a means of seeking God to the exclusion of all else. Fasting does not cast out demons but rather, it casts out unbelief. Fasting is beneficial in every aspect of the Christian life - not only in the casting out of devils.
The real virtue of a fast is in humbling ourselves through self denial (Ps. 35:13; 69:10), and that can be accomplished through ways other than total abstinence. Partial fasts can be beneficial, as well as fasts of our time or pleasures. However, because appetite for food is one of man's strongest drives, fasting from food seems to get the job done the quickest. Fasting should be a much more important part of our seeking God. "Enjoy Your Coffee" by Andrew Wommack
Michael Stanley, 55