Riccati equation

Let $\mathbb{T}$ be a time scale. The Riccati equation is the nonlinear dynamic equation defined by $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ where $p(t)+\mu(t)z(t)>0$ for all $t \in \mathbb{T}^{\kappa}$.