When someone is fasting a "taanis yachid" (individual fast) he must be "m'kabel" (accept upon himself) the fast from the day before in the Tefillah of Mincha. Is the same true for the fast that one makes on the day his Mother or Father past away (See the Rema in Yoreh Deah Siman 402 Sif 12 that says it's a mitzvah to fast on this day.)
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The Kitzur Shulchan Aruch in 221:1 says that those who always fast on a Yahrzeit have the Din of one who made a Neder to fast.
Such a person does not need to accept the fast the day before, the same way those who fast at other known times - e.g. Selichot or Erev Rosh Hashana - don't have to, as is implied in Siman 127:3.