Pegasus use SAW as their hub so you'll most likely change planes there. An hour and 55 minutes should be OK.
If however, you've got to change from IST to SAW or vice versa, you'll need to allow at least that amount of time just for the transfer.
Like Easyjet, Pegasus are a budget airline. Depending on where you want to fly from, it might be worthwhile considering paying a little extra for a free meal, free drinks, extra leg-room etc with Turkish Airlines.