Certain Properties and Characterizations of Two-Iterated Two-Dimensional Appell and Related Polynomials via Fractional Operators

Abstract

This paper introduces the operational rule for 2-iterated 2D Appell polynomials and derives its generalized form using fractional operators. It also presents the generating relation and explicit forms that characterize the generalized 2-iterated 2D Appell polynomials. Additionally, it establishes the monomiality principle for these polynomials and obtains their recurrence relations. The paper also establishes corresponding results for the generalized 2-iterated 2D Bernoulli, 2-iterated 2D Euler, and 2-iterated 2D Genocchi polynomials.

Keywords

• hybrid special polynomials
• monomiality principle
• explicit form
• symmetric identities
• summation formulae
• operational connection