At the moment, a user can use the following query
created > "2014-08-21 15:00" and created < "2014-08-21 23:00"
This will return all issues created between 3pm - 11pm for that particular date.

However, a user must edit the query daily if he wants to display issues created between 3pm-11pm for the date he runs the query.

Maybe add the following syntax in JQL
created > "15:00" and created < "23:00" or
created > "today() 15:00" and created < "today() 23:00"

This will display issues created between 3pm-11pm today.

This search will be dynamic and the user will not have to edit the query