iPad 2 gives alert with no notification
iPad 2 16gb will frequently make the tri-tone sound but no notification.
iPad, iOS 8.1.3
Assumption: When you say "no notification", I assume you have opened Notification Center and checked there and confirmed there is no notification. If not, do that first.
If this happened to me, I would check each and every app (whether supplied by Apple or not) looking for a "badge" -- one of those numbers in a red circle indicating the need for some action.