Are there specific recommended acts of worship during the months of Rajab and Sha'ban? If so, what are they?

No specific virtue has been established for a particular act of worship in the month of Rajab, except for what has been narrated concerning the virtue of fasting in the sacred months. All other narrations attributed to the Prophet, peace and blessings be upon him, regarding Rajab are weak or fabricated. As for the month of Sha'ban, it is desirable to fast frequently therein, following the example of the Prophet, peace and blessings be upon him. A special virtue has also been reported for the night of mid-Sha'ban, without specifying a particular act of worship for it. Increasing worship and drawing closer to Allah is encouraged at all times and in all circumstances.