Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$

In this paper, we first reconsider Sabban frame of curves on $2-$sphere $S^{2}$ in $\mathbb{R}^{3}$ with the help of the properties of quaternion algebra and then, we define two different types of quaternionic Sabban frame of the curves on $3$-sphere $S^{3}$ in $\mathbb{R}^{4}$. Also, we support the theory in the paper with some examples.