Structured　frames　such　as　wavelet　and　Gabor　frames　in　L2(R)　have　been　extensively　studied.　But　L2(R+)　cannot　admit　wavelet　and　Gabor　systems　due　to　R+　being　not　a　group　under　addition.　In　practice,　L2(R+)　models　the　causal　signal　space.　The　function-valued　inner　product-based　Fa-frame　for　L2(R+)　was　first　introduced　by　Hasankhani　Fard　and　Dehghan,　where　an　Fa-frame　was　called　a　function-valued　frame.　In　this　paper,　we　introduce　the　notions　of　Fa-equivalence　and　unitary　Fa-equivalence　between　Fa-frames,　and　present　a　characterization　of　the　Fa-equivalence　and　unitary　Fa-equivalence.　This　characterization　looks　like　that　of　equivalence　and　unitary　equivalence　between　frames,　but　the　proof　is　nontrivial　due　to　the　particularity　of　F-a-frames.