From The Christian’s Daily Walk
All who are able should keep a public fast
All whom lawful authority enjoins, are to keep a pubic fast, Joel 1:14, so far as health will permit.
Children should not fast
Such as are of understanding; else how can they search out their ways, judge themselves, or pray? In public fasts, if authority think fit, little children may be caused to fast, that the parents, and others of understanding, may (as by objects of misery) be stirred up to a more thorough humiliation; but, in private, children and idiots [ignorant/mentally limited] are to be exempted.
The young in faith generally should not fast
Novices and unexperienced Christians are not usually to fast in private; such were Christ’s disciples, Matt 9:14, 16, 17; Luke 5:33, 34, 35, etc. When exception was taken at our Saviour, because they fasted not, he excuses them, not only that it was unseasonable to fast in a time of joy, while he, the bridegroom, was with them, but [also] because they were not able to bear so strong an exercise. (They were like old vessels and old garments, which would have been made worse rather than better by the new wine, or new cloth of fasting.) Strong physic is good, but not for babes.
There is not the same reason why they [i.e., those young in the faith] may fast in private as in public, because the minister, by teaching them and by praying with them, and for them, taketh from them the greatest part of the burden of the fast in private.
Those under care should not fast when forbidden by their superior
All such as are not in their own power, are not to keep a private fast, when those under whose power they are shall expressly contradict it. For the husband might disallow the vow of his wife, even that wherewith she had bound herself to afflict her soul by fasting, Num 30:3-8, 13. Wherefore none may fast against the will of those who have full power to command their service and attendance.