Abstract
In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form
{u(Delta)(t) = Au(t) + f(t), t is an element of T, t > t(0) u(t(0)) - x is an element of D(A),
and
{u(Delta)(t) = Au(t) + f(t,u), t is an element of T, t > t(0) u(t(0)) = x is an element of D(A),
in terms of the stability of the homogeneous equation
(u(Delta)(t) = Au(t), t is an element of T, t > t(0) u(t(0)) = x is an element of D(A),
where f is rd-continuous in t is an element of T and with values in a Banach space X, with f (t,0) = 0, and 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 X into itself. Here D(A) is the domain of A and T subset of R->= 0 is a time scale which is an additive semigroup with 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 illustrative examples.