I'm didn't use the but GRASS GIS has a lot of modules dealing with landscape analysis. Please have a look here: http://grass.osgeo.org/grass70/manuals/raster.html and search for the modules called r.li.* . Moreover probably you can use them exploiting the QGIS processing plugin.
I suggest use ht-index to measure the fragmentation, since there surely far more small patches than large ones; the higher the ht-index, the more complex or diverse the fragmentation.
Well, I tried to use GRASS plugin but I got the error message ' cannot activate grass' :(. Currently, I am looking for a solution in some forums. Do you know how to solve this problem?
Actually the r.li suite is based on FRAGSTATS. Concerning the "the error message" (@Mohamed), it might be due to installation issues. If you operate on a windows system check a) if all prerequisites has been inslalled - some libraries are needed in order to run grass and b) that the installation paths does not include spaces or non latin letters in their names. If you oparate a linux system check the dependancies for your QGIS installation.