What is the ruling on fasting supererogatory fasts (Mondays and Thursdays) in the months of Rajab and Sha’ban only, to the exclusion of other Arab months, and is this considered an innovation (bid’ah)?

It is recommended to fast on Mondays and Thursdays throughout the year, unless these days coincide with days when fasting is forbidden. Authentic hadiths have been reported about the Prophet, peace and blessings be upon him, increasing his fasting in Sha'ban, and fasting in the sacred months, including Rajab. There is no harm in limiting fasting to these two days in these two months. The correct view is the permissibility of fasting in the second half of Sha'ban for those who did not connect their fasting with the first half of it.