Are there any authentic hadiths regarding the virtue of fasting in Rajab and Sha'ban?

The questioner : In the name of Allah, the Most Gracious, the Most Merciful.
May Allah forgive you, O honorable Shaykh. Are there any authentic, established hadiths regarding the virtue of each of the months of Rajab and Sha'ban?

The Shaykh : Virtue in what?

The questioner : The virtue of each of the months of Rajab and Sha'ban, and the virtue of fasting in them?

The Shaykh : No, no authentic hadith has been narrated regarding the virtue of Rajab. The best that has been narrated about it, as Shaykh al-Islam (may Allah have mercy on him) said, is that the Prophet (peace and blessings be upon him) used to say when Rajab entered: However, this hadith is also subject to criticism. Therefore, the month of Rajab does not stand out from Jumada al-Akhirah, which precedes it, except that it is one of the sacred months. Otherwise, there is no prescribed fasting in it, no prescribed prayer, no prescribed 'Umrah, and nothing else; it is like the other months. As for Sha'ban, yes, it stands out from the others in that the Prophet (peace and blessings be upon him) used to fast frequently in it, and he would even fast the entire month except for a little. One should increase fasting in Sha'ban.