Recently,　Gabor　analysis　on　locally　compact　abelian　(LCA)　groups　has　become　the　focus　of　an　active　research.　In　practice,　the　time　variable　cannot　be　negative.　The　half　real　line　+　=　(0,∞)　is　an　LCA　group　under　multiplication　and　the　usual　topology,　with　the　Haar　measure　dμ　=　dx　x.　This　paper　addresses　Gabor　frame　multipliers　and　Parseval　duals　for　L2(+,dμ).　We　introduce　and　characterize　Gabor　frame　multipliers　and　Parseval　Gabor　frame　multipliers　based　on　Zak　transform　matrices.　Our　Zak　transform　matrix　is　essentially　different　from　the　conventional　Zibulski-Zeevi　matrix.　It　allows　us　to　define　Gabor　frame　generators　by　designing　suitable　matrix-valued　functions　of　finite　size.　We　also　prove　that　an　arbitrary　Gabor　frame　(g,a,b)　admits　a　Parseval　dual　frame/tight　dual　frame　whenever　ln　a　ln　b　are　rational　numbers　not　greater　than　1　2.　　©　2024　World　Scientific　Publishing　Company.