This looks to be a Waveshare 7" touchscreen which I recently bought as well. I had some problems with the kernels that they provided in that they disabled my GPIO access from python, but I found someone who wrote there own drivers for this. See this answer for a link to the driver and see if it works for you:
Touchscreen drivers disable GPIO interface in Python
They tested it for Raspbian-Wheezy, and thats what I used in on too, but maybe it'll work for other distributions. You may be able to contact the driver's creator too for more functionality.