Dynamic equation for nabla cosh and nabla sinh

Theorem

If $\gamma > 0$ with $\alpha^2\nu \in \mathcal{\nu}$, a regressive function, then the dynamic equation $$y^{\nabla \nabla}-\gamma^2 y=0$$ is solved by the functions $\widehat{\cosh}_{\gamma}(\cdot,s)$ and $\widehat{\sinh}_{\gamma}(\cdot,s)$, where $\widehat{\cosh}_{\gamma}$ denotes the nabla cosh and $\widehat{\sinh}_{\gamma}$ denotes the delta sinh.