First off what type of applique are you doing, turned edge, freezer paper, interfacing, raw edge, fusible web. Some methods are more prone to fraying. Also what type of stitching are you doing around applique, satin, blanket, blind hem. The best thing to do with applique is always make the background block larger than the finished block to allow for the shrinkage because you can always trim to size but you can't make a block bigger. If you want less fraying than you need to do turned edge. There are many methods like freezer paper method, starch template method, fusible interfacing method. With fusible web you are going to get fraying unless you use a satin stitch, any other stitch when washed will have some fraying around the raw edges. I haven't done too much applique, but I agree it can be frustrating especially when learning it and I am still a newbie in it. I still have my best friend wedding present unfinished because I got frustrated but hop to pick it up soon and finish. If you do choose to do the interfacing method test it out first because my finished pieces somehow ran smaller than the actual finished size and I had to scrap all the pieces I made because they were to small. Lost hours of time.