  The aim of this paper is to investigate and introduce some new identities
related to the unification and generalization of the three families of
generalized Apostol type polynomials, which are Apostol-Bernoulli,
Apostol-Euler, and Apostol-Genocchi polynomials, on the modern theory of the
Umbral calculus and algebra. We also introduce some operators. Recently, Ozden
constructed generating function of the unification of the Apostol type
polynomials (see Ozden [H. Ozden, AIP Conf. Proc. 1281, (2010), 1125-1227.]).
By using this generating function, we derive many properties of these
polynomials. We give relations between these polynomials and Stirling numbers.
