One cannot take on a fast of a few hours and call it a fast - it doesn't count in that regard. And separating from a community fast is not acceptable either - so joining in a small part of that fast in solidarity is, however, acceptable. With supports and arguments against this position regarding partial fasts. Including a rule of thumb making sure that one takes a fast upon oneself from the day before. When exactly? It's a machloket, though pegged to the afternoon. Plus, an important turning to Megilat Taanit, as the official calendar of holidays. Also, the case of high quality meat enticing someone who is fasting, and when whether one can break the fast and make it up another time, based on how badly you want to eat it. Plus, a "fast because of a dream," to provide an antidote, as it were, for a bad dream (even on Shabbat). Plus, a new mishnah: more serious fasting for rain by the community. Which includes limiting activity as well. Where fasting isn't fasting, as we like to say.