Stability of abstract dynamic equations on time scales

In this paper, we investigate many types of stability, like uniform stability, asymptotic stability, uniform asymptotic stability, global stability, global asymptotic stability, exponential stability, uniform exponential stability, of the homogeneous first-order linear dynamic equations of the form x(Delta)(t) = Ax(t), t > t(0), t, t(0) is an element of T x(t(0)) = x(0) is an element of D(A), where A is the generator of a C-0-semigroup {T(t) : t is an element of T} subset of L(X), the space of all bounded linear operators from a Banach space X into itself. Here, T subset of R->= 0 is a time scale which is an additive semigroup with the property that a - b is an element of T for any a, b is an element of T such that a > b. Finally, we give an illustrative example for a nonregressive homogeneous first-order linear dynamic equation and we investigate its stability.