Function bounds for solutions of Volterra integro dynamic equations on time scales

Abstract

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases $\mathbb{T}=\mathbb{R}$ and $\mathbb{T}=\mathbb{Z}$. Extending the scope of time scale variant of Gronwall's inequality we determine function bounds for the solutions of the integro dynamic equation.