Yes if you mean the thin mat type that comes in rolls like carpet. I used that type inside of a screened in country style porch and I used one of these carpet stretchers to get it tight just be careful because the style of artificial turf I used wore thin quickly in areas that I had stretched it the most.
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This does not have a fastner to it. If you are referring to what holds the carpet it place, there are tack strips at the edge of the carpet that hold it in place. This stretches the carpet past its current position on the tacks so that the carpet becomes more taught. I pushed with the kicker and pressed the carpet down on the tack strips. If the carpet moved enough, you can feel the tacks bite into the underside of the carpet when you push down (and sometimes you can hear it too). If you are installing new carpet and don't have tack strips, you'll need to purchase some for the perimeter of the carpet. The come in packs and are pretty cheap. You nail them down with the tacks facing up (or you can screw them down after pre-drilling). Then you can lay your carpet. I hope this helps!
The Home Depot does have a very good toll rental program and although you will have to check availability in your area I am almost certain that you'll be able to rent one near you.