Waalaikumsalam, Month of Rajab is one month of Muharram, which means dimulyakan (There are 4 months: Dzulqa'dah, Dhu al-Hijjah, Muharram, and Rajab). Fasting in the month of Rajab, as in other mulya months, is Sunnah.
It was narrated from al-Bahiliyah Mujibah, he said: "Puasalah in the months haram (mulya)." (Reported by Abu Dawud, Ibn Majah, and Ahmad). Another Hadith is the history of al-Nasa'i and Abu Dawud (and validated by Ibn Huzaimah): "Osama said the Prophet, 'O Messenger of Allah, I do not see the Prophet fasting (circumcision) as much as the Apostles did in the month of Ramadhan. ' The Apostle replied: 'Month of Ramadhan is the month of Rajab and Ramadan which is forgotten by most people.' "
According to al-Syaukani (Naylul Authar, on the subject of circumcision fasting) expression of the Prophet "Month Ramadhan is a month between Rajab and Ramadan which most people forget" it implicitly suggests that the month of Rajab is also Sunnah to fast on it.
