Based on the fact that the quantum mechanical version of Hankel transform keel(the Bessel function)is just the transform between |q,r> and(s,r′|,two induced entangled state representations are given,and working with them we derive fractional squeezing-Hankel transform(FrSHT)caused by the operator e-iα(a?1a?2 +a1a2)e-iπa?2a2,which is an entangled fractional squeezing transform operator.The additive rule of the FrSHT can be explicitly proved.