Tighter monogamy and polygamy relations using Rényi-$\alpha$ entropy

We investigate monogamy relations related to the Rényi-$\alpha$ entanglement and polygamy relations related to the Rényi-$\alpha$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $\mu$th power of Rényi-$\alpha$ entanglement with $\alpha \in \left[\right(\sqrt{7}-1)/2,(\sqrt{13}-1\left)/2\right]$ for $\mu \ge 2$, and polygamy relations satisfied by the $\mu$th power of Rényi-$\alpha$ entanglement of assistance with $\alpha \in \left[\right(\sqrt{7}-1)/2,(\sqrt{13}-1\left)/2\right]$ for $0\le \mu \le 1$. These relations are shown to be tighter than the existing ones.