Is fasting on the 1st of Rajab encouraged based on the practice of the Prophet, sallallaahu alayhi wa sallam?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Singling out the first of Rajab or the first three days of this month is an innovation. There is no evidence from the Prophet that proves fasting in Rajab, except that it is one of the four sacred months in which fasting is desirable. Therefore, believing desirability of fasting in this month is a deviation and a mistake. This is one of the innovations of the month of Rajab like performing a special 'Umrah in this month or worshipping in the night of the first Friday of this month, called 'The night of Al-Raghaa'ib'. All these matters are not proved from the Prophet and there is no basis for that in Islam.

Allaah Knows best.