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In this paper, we first generalize the theorem about the existence of anenveloping action to a partial twisted smash product. Second, we construct aMorita context between the partial twisted smash product and the twisted smashproduct related to the enveloping action. Furthermore, we show some resultsrelating partial actions and partial representations over the partial twistedsmash products, which generalize the results of Alves and Batista (Comm.Algebra, 38(8): 2872-2902, 2010). Finally, we present versions of the dualitytheorems of Blattner-Montgomery for partial twisted smash products.

Enveloping actions and duality theorems for partial twisted smash products