We apply a new definition of periodicity on isolated time scales introduced
by Bohner, Mesquita, and Streipert to the study of Ulam stability. If the graininess (step
size) of an isolated time scale is bounded by a finite constant, then the linear 1- and
2-periodic dynamic equations are Ulam stable if and only if the exponential function
has modulus different from unity. If the graininess increases at least linearly to infinity,
the 1- and 2-periodic dynamic equations are not Ulam stable. Applying these results, we
give several interesting examples of first-order linear 1- or 2-periodic dynamic equations
on specific isolated time scales such as h-difference equations, q-difference equations,
triangular equations, Fibonacci equations, and harmonic equations. In some cases the
minimum Ulam stability constant is found.
