Q. See question above. Is there value to fasting until chatzos on Bahav and or diminishing food in ones meals?

A. Maseches Sof’rim ( 21) mentions that there were talmidim who fasted on a Monday, Thursday, and following Monday in the month of Nisan. However, it is clear that this was a private practice which was not publicized.

Tur (O.H. 492) mentions the custom of Ashkenazim to fast in Cheshvan and Iyar. In later generations, this custom spread to some Sephardic communities. (Kneses Hagedola 492)
Some explain that the reason for the fasts is in case one sinned over the long Sukkot or Pesach holidays, and others say that it should be for an atonement before the raining and harvest seasons. The days of Monday and Thursday were chosen because they are considered days of extra mercy from Heaven.

Following the Mishna Berurah (492: 3), the fasts should always be on the first Monday, Thursday, and following Monday, following the first Shabbos after Rosh Chodesh Cheshvan and Iyar. However, some communities have the custom to delay the fasts in Cheshvan until the end of the month. Since Shavuot is only one day (or two days in the Diaspora), there is less of a concern that one sinned, and there was no widespread custom to fast after Shavuos. Nevertheless, there have been individuals who fasted on a Monday, Thursday and Monday after Shavuot.

Traditionally, on the Sabbath preceding these fasts, a special Mi Shebeirach is recited for those who intend to fast.[6] Most communities recite this Mi Shebeirach before returning the Sefer Torah to the Ark, but some (generally Western European communities) add it as an additional line to the Mi Shebeirach recited for the community (after Yekum Purkan). One who responds “Amen” to this blessing does not need to accept the fast upon oneself at the Mincha of the proceeding day.
While today few people fast, there are many communities which say selichos.

Rabbi A. Bartfeld as revised by, Horav Dovid Pam, Horav Aharon Miller, Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit’a