Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials

This article aims to identify the generating function of modified Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modified Apostol type q-Bernoulli polynomials are given. It is shown that aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications on q-Umbral calculus. From those applications, we derive some theorems in order to get Apostol type modified q-Bernoulli polynomials as a linear combination of some known polynomials which we stated in the paper.