In addition to the suggestions already made (great suggestions!), you could also do something on the order of a duvet cover, looking at this as an opportunity to freshen up the decor in your room and possibly adding some cotton containing fabric for comfort. Some thrift store curtains might contain the fabric you need cheaply. I have taken a quilt that was given to me and made coordinating pillow shams to use it for my bedspread. If you don't sew, you might be able to find duvet cover in a clearance section. Alternatively, if the fraying is on an edge, you could cover it with a wide blanket binding around the edge, even using some iron on seam tape if you don't sew.
If sewing is not an issue, perhaps if one corner is frayed, you could cover all four corners in a fabric you like to make it look deliberate. Or if it is not conveniently located, coming up with a unique applique might add to it. For example, my husband needed some knee patches for his jeans, so I used some other Jeans with bad knees to turn them into shorts and use the excess material to patch his knees in a skull applique (making it more interesting for both of us.) If you are worried about your
art work, just make a pattern by printing out a general pattern from the internet. Coloring book like pictures make great applique patterns with their simple lines.