Currently, when performing a Basic Search for the Created Date of issues in JIRA, the times of the days are assumed and cannot be modified. This can lead to confusion for the following reason:

Let's say a user wants to search for all issues created between the start of the day on June 25th, and the end of the day of June 27th. A user would likely put those two dates in the basic search on Created Date (Between dates June 25th through June 27th). This would yield the following JQL:

created >= 2016-01-25 AND created <= 2016-01-27

In JQL, 'created' assumes the time of 00:00 unless specified otherwise (which cannot be done in the basic search), which would mean that their search yields:

created >= "2016-01-25 00:00" AND created <= "2016-01-27 00:00"

Unless a ticket was created on midnight of the 27th, that entire day will not be included in the search. A majority of users would expect the basic search to yield the following advanced JQL instead:

created >= "2016-01-25 00:00" AND created <= "2016-01-27 23:59"

Without being able to specify the times of day in the basic search, only assumed times are used, and if a user doesn't know to configure the JQL in advanced search or search a day above the results they need, they will not be seeing all of the issues they are looking for.