The month of Sha`ban is a beloved month for Muslims, for it precedes the month of Ramadan. In addition, the Prophet (peace and blessings be upon him) is reported to have observed optional fasting in this month more than in any other month.
Sheikh ibn Fawzan, states the following: Nothing firm and reliable has been established on the authority of the Prophet (peace and blessings be upon him), that he held night vigil prayer and fasted during the day of the 15th of Sha`ban. So, the night of the 15th of Sha`ban is like any other night, and if someone regularly observes acts of worship during other nights, then he may hold night vigil prayer on this night without assuming anything special (because of it being the night of the 15th of Sha`ban).
this is because specifying a time for any act of worship requires an authentic proof, so if there is no authentic proof then the act is regarded as an innovation and all innovations are misguidance. Likewise, regarding specifically fasting during the 15th day of Sha`ban, then no (authentic) proof has been established on the authority of the Prophet (peace and blessings be upon him) to indicate the legality of fasting on that particular day.
Sheikh ibn `Uthaymeen, adds: What is correct is that fasting on the 15th of Sha`ban or specifying it with reciting (the Qur’an) or making (particular) supplications on that day has no basis. So that day is like any other 15th day of other months. Something that is clear is that it has been made permissible for a person to fast on the 13th, 14th, and 15th of every month. However, Sha`ban is somehow special (except for Ramadan) in the sense that the Prophet (peace and blessings be upon him) used to fast more in the month of Sha`ban than any other month. So he used to either fast all of Sha`ban or just a little.
therefore, as long as it does not involve any hardship, one can increase his fasting days during Sha`ban, emulating the example of the Prophet (peace and blessings be upon him).