In this paper we investigate the fractional quantum correlations via squashed entanglement and negativity, where an analytical solution of a fractional Schrödinger equation under an XXX model of a spin-spin Hamiltonian has been introduced. It has shown that, by starting with an initially large entangled state, both quantifiers decrease during the interaction. This decay increases as one increases the degree of the fractional order and the coupling constant between the two spins. However, the squashed entanglement and the negativity increase gradually if the initial state contains a small amount of quantum correlations. The sudden/gradual changes of these phenomena have been observed at small/large values of the fractional order, respectively. The constant behavior of these measures is observed at small values of fractional orders. Our results show that the fractional state can be used as a quantum channel with high efficiency to perform quantum teleportation. The long-lived constant behavior of the teleportation inequality indicates that the efficiency of this channel will be constant during the teleportation process.