actually, Jesus said prayer and fasting helps you with your own 'natural' unbelief; all demons come out by faith in His delegated authority to you over the devil and his bunch:
Mat 17:19-21 KJV
(19) Then came the disciples to Jesus apart, and said, Why could not we cast him out?
(20) And Jesus said unto them, Because of your unbelief: for verily I say unto you, If ye have faith as a grain of mustard seed, ye shall say unto this mountain, Remove hence to yonder place; and it shall remove; and nothing shall be impossible unto you.
(21) Howbeit this kind goeth not out but by prayer and fasting.
the subject of verse 20 is unbelief; so 'this kind' in verse 21 refers to a form or kind of unbelief - He wasn't talking about demons in verse 21.
for the reborn believer, fasting is how you train yourself to not be moved by the reports of your flesh. looking back at the example of the lunatik son in Mat 17, the boy rolled around on the ground and foamed at the mouth in front of the disciples, and this display moved them to doubt their authority over this particular demon. as you fast, you deny your body's 'reports', and this helps you to not be moved by what you perceive with your 5 senses.
fasting isn't restricted to food; you can fast from carnal tv shows and music, newspapers, traditions (things you do without checking with God first) - anything in the natural realm that distracts you from His word (the spiritual realm). be very careful of prolonged food fasting as this has killed many.
God's chosen fast:
Isa 58:5-12 KJV
(5) Is it such a fast that I have chosen? a day for a man to afflict his soul? is it to bow down his head as a bulrush, and to spread sackcloth and ashes under him? wilt thou call this a fast, and an acceptable day to the LORD?
(6) Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke?
(7) Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?
(8) Then shall thy light break forth as the morning, and thine health shall spring forth speedily: and thy righteousness shall go before thee; the glory of the LORD shall be thy rereward.
(9) Then shalt thou call, and the LORD shall answer; thou shalt cry, and he shall say, Here I am. If thou take away from the midst of thee the yoke, the putting forth of the finger, and speaking vanity;
(10) And if thou draw out thy soul to the hungry, and satisfy the afflicted soul; then shall thy light rise in obscurity, and thy darkness be as the noonday:
(11) And the LORD shall guide thee continually, and satisfy thy soul in drought, and make fat thy bones: and thou shalt be like a watered garden, and like a spring of water, whose waters fail not.
(12) And they that shall be of thee shall build the old waste places: thou shalt raise up the foundations of many generations; and thou shalt be called, The repairer of the breach, The restorer of paths to dwell in.