اسلام عليكما 
Is there Fasting Month of Rajab?

There is no special practice related Rajab , both its form of prayer, fasting, zakat, or umrah. The majority of scholars explain that the hadith which mentions the practice in Rajab is the hadith is weak and rejected.
Ibn Hajar said,

لم يرد في فضل شهر رجب, ولا في صيامه, ولا في صيام شيء منه معين, ولا في قيام ليلة مخصوصة فيه حديث صحيح يصلح للحجة, وقد سبقني إلى الجزم بذلك الإمام أبو إسماعيل الهروي الحافظ
"There is a legitimate history liveable 'arguments about the virtues of Rajab, nor a history that is authentic about rajab fasting, or fasting in Rajab certain date, or specific prayers at night tahajud rajab month. My statement has been preceded by a description of Imam Al-Haafiz Abu Ismail Al-Harawi. "(Tabyinul ujub bi Warada Ma fi Fadl Rajab, p. 6)
The same statement was also delivered by Imam Ibn Rajab. In his work that explores the practice throughout the year, entitled Lathaiful Maarif, he insists there is no sunnah prayer for the month rajab,
لم يصح في شهر رجب صلاة مخصوصة تختص به و الأحاديث المروية في فضل صلاة الرغائب في أول ليلة جمعة من شهر رجب كذب و باطل لا تصح و هذه الصلاة بدعة عند جمهور العلماء
"There are no valid arguments about the specific recommendation prayers in the month of Rajab. As for the hadith which states the primacy of prayer Raghaib on the first Friday night of Rajab is the tradition of lies, vanity, and is not valid. Salah Raghaib is heresy, according to the majority of scholars. "(Lathaiful Maarif, p. 213)
Related problems of fasting in Rajab, Imam Ibni Rajab also asserted,
لم يصح في فضل صوم رجب بخصوصه شيء عن النبي صلى الله عليه و سلم و لا عن أصحابه و لكن روي عن أبي قلابة قال: في الجنة قصر لصوام رجب قال البيهقي: أبو قلابة من كبار التابعين لا يقول مثله إلا عن بلاغ و إنما ورد في صيام الأشهر الحرم كلها
"None of the authentic hadith of the Prophet sallallaahu 'alaihi wa sallam about the virtues of fasting month of Rajab in particular. Only there is a history of Abu Qilabah, that he says, 'In heaven there is a palace for the diligent fasting in Rajab.'However, this is not a history of tradition. Imam Al-Bayhaqi comment on the statement of Abu Qilabah, 'Abu Qilabah including senior tabi'in. He did not convey the history, but only without a sanad news. ' The history that there is a history that says the recommended fasting entirely sacred "(Lathaiful Maarif, p. 213)
Description Ibn Rajab who advocate their fasting in the sacred months, indicated in the hadith of Al-Bahiliyah Mujibah from his father or his uncle, Al-Bahily. Sahabat Al-Bahily it came to the Prophet sallallaahu 'alaihi wa sallam, after meeting and expressed converted to Islam, he then went home village. One year later, he came back to the Prophet sallallaahu 'alaihi wa sallam.
"O Messenger of Allah, do you still know me." ask Kahmas,
"Who are you?" Asked the Prophet sallallaahu 'alaihi wa sallam.
"I am Al-Bahily, who once came to see you a year ago." Thread friend
"What happened to you, but first you fresh body?" Asked the Prophet sallallaahu 'alaihi wa sallam.
"I've never eaten, except the night, since my separation from you." Answered friend.
Recognizing this spirit companions to fast, the Prophet sallallaahu 'alaihi wa sallam advised,
لم عذبت نفسك, صم شهر الصبر, ويوما من كل شهر
Why are you torturing yourself. Wait your fast in the month (of Ramadan), and fasting one day per month.
But Al-Bahily always ask for extra sunna fasting,
"Your fast one day each month." This person said, "I'm still strong. Increase! "" Two days every month. "This person said," I'm still strong. Increase! ' "Three days every month." People still ask to be added. Until finally the Prophet sallallaahu 'alaihi wa sallam giving Pungkasan sentence,
صم من الحرم واترك, صم من الحرم واترك, صم من الحرم واترك
"Fast in the sacred months, then do not fasting (except Ramadan) ..., fasted in the sacred months, then do not fasting ..., fasted in the sacred months, then do not be fasting." (HR. Ahmad, Abu Dawud, Al-Baihaqi and others. this Hadith deemed valid by some scholars and rated da'eef by other scholars).
Month illicit means glorious month. Allah exalted this month with a ban on fighting. Sacred months, there are four: Dzulqa'dah, Hijjah, Muharram and Rajab.

Fasting in the sacred month 

Mujibah Hadith Al-Bahiliyah tell Anjuan to fast at all the sacred months, as stated Ibn Rajab. And that's suggestion fasting as a last resort when a person wants to reproduce the sunnah fasting, as recommended by the Prophet sallallaahu 'alaihi wa sallam to his friend Al-Bahily. Therefore, too much when this tradition is used as the argument of the recommended fasting rajab specifically, while for the other sacred months, less attention. Because the practice by some scholars, they are fasting throughout the month unclean, just months rajab.As stated by Ibn Rajab,
قد كان بعض السلف يصوم الأشهر الحرم كلها منهم ابن عمر و الحسن البصري و أبو اسحاق السبيعي و قال الثوري: الأشهر الحرم أحب إلي أن أصوم فيها
Some scholars of the Salaf fasting in all the sacred months, among them: Ibn Umar, Hasan Al-Basri, and Abu Ishaq As-Subai'i. Imam Ats-Thawri said, "The months haram, more I love to be a time of fasting." (Lathaiful Maarif, p. 213).

The Friends Prohibit Specialising Rajab for fasting

Habits are fasting rajab has existed in the time of Umar radi 'anhu. Some Successors who lived in the time of Umar even have to go it. Thus, we can refer friends how attitudes towards activities related phenomena in rajab they encounter.
Here are some of the history that says their reaction to fasting rajab. This story is taken from the book Lathaiful Maarif, a special book of Ibn Rajab, which discusses wadzifah (practice the Sunnah) of all time,
روي عن عمر رضي الله عنه: أنه كان يضرب أكف الرجال في صوم رجب حتى يضعوها في الطعام و يقول: ما رجب?إن رجبا كان يعظمه أهل الجاهلية فلما كان الإسلام ترك
It was narrated from Umar radi 'anhu, that he struck the palms some people who do fasting rajab, until they lay their hands on the food. Umar said, "What rajab? Sesungguhnnya rajab is the month that first exalted ignorant society. After Islam came, abandoned. "
In another narration,
كره أن يكون صيامه سنة
"He hates it when fasting rajab made sunna (custom)." (Al-Maarif Lathaif, 215).
In another story, about Abu Bakrah companions radi 'anhu,
أنه رأى أهله قد اشتروا كيزانا للماء واستعدوا للصوم فقال: ما هذا? فقالوا: رجب. فقال: أتريدون أن تشبهوه برمضان?وكسر تلك الكيزان
He saw his family had bought the vessel to the water reservoir, they are prepared for fasting. Abu Bakrah asked: 'Fasting is this?' They said: 'Fasting rajab' Abu Bakrah replied, 'Do you want to equate rajab with Ramadan?' then he broke the jars it.(This history is mentioned by Ibnu Qudaamah in al-Mughni 3/107, Ibnu Rajab in Lathaif pp. 215, Shaikh-ul-Islam in Majmoo 'Fatawa 25/291, and Al-Haafiz ibn Hajar in Al-UJB Tabyi p. 35)
Ibnu Rajab also mentions some other history of some other friends, such as Ibn Umar and Ibn Abbas, that they hate someone who fasted rajab full month.
Their attitude shows that they understand the moon month rajab not recommended to be used specifically fasting time. Because the habit is very likely, they are not experienced at the time of the Prophet sallallaahu 'alaihi wa sallam.
Conclusion:
The conclusion from the foregoing,
  1. There were no specific mention proposition rajab virtue month.
  2. Not found proposition that the virtue of fasting or praying sunnah rajab specialized in rajab.
  3. Some friends prohibit specialize specifically in the month of fasting or fasting rajab full month during the months rajab.
  4. Proposition that a special virtue for those who do fasting rajab is hadith is weak, and can not be a proposition.
  5. For people who are diligent fasting, allowed to multiply fast in the sacred months. As stated in the hadith Al-Bahily. However, this tradition is common to all the fasting month of haram, not only rajab.
Allahu a'lam