Abstract
In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between F-n((alpha)) (x; lambda; mu, nu, c) and F-H(n)(alpha (x, y; lambda; mu, nu, c) are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.