Abstract
The present article is to introduce a new class of q-Hermite based Apostol-type polynomials and to investigate their properties and characteristics. In particular, the generating functions, series expression and explicit and recurrence relations for these polynomials are established. We derive some relationships for q-Hermite based Apostol-type polynomials associated with q-Apostol-type Bernoulli polynomials, q-Apostol-type Euler and q-Apostol-type Genocchi polynomials.