Praise be to Allaah.
There is nothing special about these particular days at all. All the days of Rajab are special, with no exception, because Rajab is one of the Sacred Months, like Dhoo’l- Qi’dah, Dhoo’l-Hijjah and Muharram.
The thirteenth day of each month - not just Rajab - is one of the three Ayyaam al-Beed (white days) on which it is encouraged to fast. These days are the 13th, 14th, and 15th of each hijri month.
Many of those who follow bid’ah (innovations) think that there is something special about certain days and do special acts of worship on those days, with no sound Islaamic basis or evidence (daleel). Their deeds are not acceptable, because they have innovated something in the religion of Allaah without the permission of Allaah.
We ask Allaah to help us follow the Sunnah and avoid bid’ah. May Allaah bless our Prophet Muhammad .