No — with Frontier Airlines you can’t bring a standard backpack as a free carry-on unless it meets their “personal item” size requirements. Only one personal item (for example a small backpack under 14″ H × 18″ W × 8″ D) is included in your fare. If your backpack is larger (i.e., overhead carry-on size: 24″ × 16″ × 10″ and ≤35 lb), you’ll need to pay the relevant carry-on bag fee.