  The purpose of this paper is to define generalized Apostol--Bernoulli
polynomials with including a new cosine and sine parametric type of generating
function using the quasi-monomiality properties and trigonometric functions. In
this study, the Apostol-Bernoulli polynomials with three variable are defined
with two new generating functions cosine and sine parameters. Then, we
investigate multiplicative and derivative operators, diffrential equations,
some summation formulas and partial differential equations for these
polynomials. Moreover, we introduce Gould--Hopper--Apostol--Bernoulli type
polynomials, Hermite--Appell--Apostol--Bernoulli type polynomials and truncated
exponential Apostol--Bernoulli type polynomials. Finally, the special cases of
these new polynomials are investigated, and the corresponding results are
expressed.
