Exponential Stability of Volterra Integro Dynamic Equations on Time Scales

In this paper, we give new sufficient conditions for boundedness and exponential stability of solutions for nonlinear Volterra integro dynamic equations from above on unbounded time scales using first Lyapunovs method. To prove this result we reduce the n-dimensional problem to the corresponding scalar one using the concept of matrix measure and a new simpler proof of Coppel’s inequality on the time scales. There is an example that illustrates the conditions of the theorem.