From A Hunger for God by John Piper, p. 103, quoting Jonathan Edwards in Some Thoughts Concerning the Revival:
One thing more I would mention concerning fasting and prayer, wherein I think there has been a neglect in ministers; and that is that although they recommend and much insist on the duty of secret prayer, in their preaching; so little is said about secret fasting. It is a duty recommended by our Savior to his followers, just in like manner as secret prayer is, … Though I don’t suppose that secret fasting is to be practiced in a stated manner and steady course as secret prayer, yet it seems to me ’tis a duty that all professing Christians should practice, and frequently practice. There are many occasions of both a spiritual and temporal nature that do properly require it; and there are many particular mercies that we desire for ourselves or friends that it would be proper, in this manner, to seek of God.