There are two methods in the MouseInfo class that detect mouse movement -- the 'mouseMoved' and the 'mouseDragged' methods. When either becomes true, get a MouseInfo object and make sure it is not a 'null' value before getting its world coordinate values to set your actor at.
If you want some commands follow the link here: link and search on the greenfoot api for 'mouse'. That should give an idea of all the methods there are which do something with the mouse.
You can search through the methods found here for methods that return various states of the mouse and also to get a MouseInfo object. And, you can go here for the MousInfo class API to see what methods are available to use on a MouseInfo object..