A Study on Generalized Degenerate Form of 2D Appell Polynomials via Fractional Operators

Abstract

This paper investigates the significance of generating expressions, operational principles, and defining characteristics in the study and development of special polynomials. The focus is on a novel generalized family of degenerate 2D Appell polynomials, which were defined using a fractional operator. Motivated by inquiries into degenerate 2D bivariate Appell polynomials, this research reveals that well-known 2D Appell polynomials and simple Appell polynomials can be regarded as specific instances within this new family for certain values. This paper presents the operational rule, generating relation, determinant form, and recurrence relations for this generalized family. Furthermore, it explores the practical applications of these degenerate 2D Appell polynomials and establishes their connections with equivalent results for the generalized family of degenerate 2D Bernoulli, Euler, and Genocchi polynomials.