The 15th of Sh'vat (Tu B'Shvat) is Rosh Hashanah for trees. We are not allowed to fast on this day because it is like a Yom Tov. Even a groom on the eve of his wedding does not fast.
--Magen Avrohom 573:3

We do not recite Tachanun on Tu B'Shvat or at the Mincha on the day before. However, we do recite Kail Erech Apayim before the removal of the Sefer Torah and La Minatzeach from the end of Shacharis. If Tu B'Shvat falls out on Shabbos, we do not recite Av Harachamim at Shacharis or Tzidkoscha at Mincha.

--Shulchan Aruch 131:6/Pri Megadim 131:14,15