Hi Wendy
When you are making your applique pieces you need to draw them on the fusible, cut out AROUND the outside of the shape, iron it onto the fabric, then cut ON the line of the applique. This way the sticky is all the way to the edge of the shape. This cuts down on fraying.
My daughter was having a fraying problem with applique and I found out she was cutting the shape out of the fusible and then ironing it onto the fabric and cutting the fabric.
I hope this helps too.