Determinant approach of the (p,q)-Hermite-Appell polynomials and some of their components

In this work, we offer the novel class of -Hermite-Appell polynomials. Some attributes of this class are constructed, along with the generating function, series definition, -derivative properties, -integral representation, summation formulas, and determinate representation. Additionally, we consider a few components for the -Hermite-Appell polynomials and infer certain elements of their traits. The generating function and series expansions of some classes of two-dimensional -Hermite-Appell polynomials are provided. Moreover, we acquire a -differential operator formula for -Hermite-Appell polynomials. Finally, the Wolfram Mathematica software is used to plot the graphical diagrams of select components of -Hermite-Appell, along with two-dimensional -Hermite-Appell polynomials.