A \(q\)-Umbral Approach to \(q\)-Appell Polynomials

In this paper we aim to specify some characteristics of the so called family of \(q\)-Appell Polynomials by using \(q\)-Umbral calculus. Next in our study, we focus on \(q\)-Genocchi numbers and polynomials as a famous member of this family. To do this, firstly we show that any arbitrary polynomial can be written based on a linear combination of \(q\)-Genocchi polynomials. Finally, we approach to the point that similar properties can be found for the other members of the class of \(q\)-Appell polynomials.