Delta exponential dynamic equation

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Theorem

Let $\mathbb{T}$ be a time scale and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following dynamic equation holds: $$y^{\Delta}(t)=p(t)y(t), \quad y(s)=1$$ is called the exponential dynamic equation. Its solution is the delta exponential.