The quick answer is yes. Arizona statutes provide that you are entitled up to three years of back child support.
The difficulty comes from two issues:
1. Determining the proper amount of support through the proof of employment or income of the other person for the previous three years and;
2. Proving or disproving a claim that support has been paid either through cash payments or by providing diapers, clothing formula etc.
In sum, you are entitled to three years back child support but, as always is the case with law, the devil is in the details.