According to a narration from Hazrat Ali (RA) in Sunan Ibn Majah (Hadith No. 138) Prophet Muhammad (PBUH) said: "When the night of the fifteenth of Shaban comes, stand in prayer in that night (qiyam) and fast on that day."
Therefore, it is recommended to fast on the fifteenth of Shaban. If someone does so, they will be rewarded, and if they do not, there is no sin.