If it is EPDM rubber you can use the EPDM based rubber roof coats available in most home and hardware stores. Kool Seal is one common brand.
I can't imagine what sort of roof looks like shingles. Is it some sort of overlapping layers, which is what I think of with a shingle roof? The "looks like fiberglass strands" suggests an EPDM rubber roof where the rubber has eroded away and left the woven fabric base exposed.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL