Fasting prayer is thought be more sincere than just praying by some Christians.
That belief is based on the following excerpt from the book of Matthew, this particular saying of Jesus is not included in any other Gospel.
Matthew 17:15 through 21 NRKJV
15 Lord, have mercy on my son: for he is lunatick, and sore vexed: for ofttimes he falleth into the fire, and oft into the water.
16 And I brought him to thy disciples, and they could not cure him.
17 Then Jesus answered and said, O faithless and perverse generation, how long shall I be with you? how long shall I suffer you? bring him hither to me.
18 And Jesus rebuked the devil; and he departed out of him: and the child was cured from that very hour.
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.