If you want to make a personal fast day on a Sunday, are you allowed to be Mekabel the fast on Shabbos?
You may be mekabel the fast on Shabbos, in fact we do this on shabbos before fasting “bahab”. One of the reasons given for this is because it is not preparing anything physical, but rather that the person is not eligible to fast. Similar to when a person prepares the torah reading for the next day. It is permitted because we look at it that the person is now better because he knows the torah reading.
Tosafos Avodah Zara 34a D”H Misanin, S”A O”C. 562 Sharrie Teshuva 2, M”B 38, Knei Bosem 2-10.