Studies on Special Polynomials Involving Degenerate Appell Polynomials and Fractional Derivative

Wani, Shahid Ahmad; Abuasbeh, Kinda; Oros, Georgia Irina; Trabelsi, Salma

doi:10.3390/sym15040840

Cited by 7 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Inspiring research can be read regarding this topic, such as in [29] or [30]. Fractional calculus aspects could also be added into studies, as is seen in very recent publications like [31] or [32].…”

Section: Discussionmentioning

confidence: 99%

Exploring the Characteristics of Δh Bivariate Appell Polynomials: An In-Depth Investigation and Extension through Fractional Operators

Almusawa

2024

Fractal Fract

View full text Add to dashboard Cite

The objective of this article is to introduce the ∆h bivariate Appell polynomials ∆hAs[r](λ,η;h) and their extended form via fractional operators. The study described in this paper follows the line of study in which the monomiality principle is used to develop new results. It is further discovered that these polynomials satisfy various well-known fundamental properties and explicit forms. The explicit series representation of ∆h bivariate Gould–Hopper polynomials is first obtained, and, using this outcome, the explicit series representation of the ∆h bivariate Appell polynomials is further given. The quasimonomial properties fulfilled by bivariate Appell polynomials ∆h are also proved by demonstrating that the ∆h bivariate Appell polynomials exhibit certain properties related to their behavior under multiplication and differentiation operators. The determinant form of ∆h bivariate Appell polynomials is provided, and symmetric identities for the ∆h bivariate Appell polynomials are also exhibited. By employing the concept of the forward difference operator, operational connections are established, and certain applications are derived. Different Appell polynomial members can be generated by using appropriate choices of functions in the generating expression obtained in this study for ∆h bivariate Appell polynomials. Additionally, generating relations for the ∆h bivariate Bernoulli and Euler polynomials, as well as for Genocchi polynomials, are established, and corresponding results are obtained for those polynomials.

show abstract

Section: Discussionmentioning

confidence: 99%

Exploring the Characteristics of Δh Bivariate Appell Polynomials: An In-Depth Investigation and Extension through Fractional Operators

Almusawa

2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Furthermore, in the literature, we find the use of a certain degenerate differential and degenerate difference operator to study the degenerate harmonic numbers and some properties of the degenerate Laguerre polynomials [7]. We also found a study on a new generalized family of degenerate three-variable Hermite-Appell polynomials defined using a fractional derivative [30]. The polynomials and Korobov numbers, some properties, identities, recurrence relations, connections with other polynomials, and some of their generalizations in different contexts have also been studied by several authors using umbral calculus [5,15,23].…”

Section: Introductionmentioning

confidence: 94%

On new generalized discrete U -Bernoulli-Korobov-kind polynomials and some of their properties

Urieles,

Escalante,

Ortega

2024

J. Math. Computer Sci.

View full text Add to dashboard Cite

“…The foundation for a more thorough understanding of the monomiality principle and its use in the context of hybrid special polynomials was laid by their combined contributions. According to studies like [10][11][12][13][14][15][16][17], unique categories of hybrid special polynomials connected to Appell sequences have been created and thoroughly investigated, endowing these polynomials with significant utility in a variety of domains. These areas cover engineering, biological sciences, medicine, and physical sciences, where these polynomials have important applications.…”

Section: Introductionmentioning

confidence: 99%

Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials

Wani,

Oros,

Mahnashi

et al. 2023

Mathematics

Self Cite

View full text Add to dashboard Cite

The evolution of a physical system occurs through a set of variables, and the problems can be treated based on an approach employing multivariable Hermite polynomials. These polynomials possess beneficial properties exhibited in functional and differential equations, recurring and explicit relations as well as symmetric identities, and summation formulae, among other examples. In view of these points, comprehensive schemes have been developed to apply the principle of monomiality from mathematical physics to various mathematical concepts of special functions, the development of which has encompassed generalizations, extensions, and combinations of other functions. Accordingly, this paper presents research on a novel family of multivariable Hermite polynomials associated with Frobenius–Genocchi polynomials, deriving the generating expression, operational rule, differential equation, and other defining characteristics for these polynomials. Additionally, the monomiality principle for these polynomials is verified, as well as establishing the series representations, summation formulae, operational and symmetric identities, and recurrence relations satisfied by these polynomials. This proposed scheme aims to provide deeper insights into the behavior of these polynomials and to uncover new connections between these polynomials, to enhance understanding of their properties.

show abstract

Studies on Special Polynomials Involving Degenerate Appell Polynomials and Fractional Derivative

Cited by 7 publications

References 20 publications

Exploring the Characteristics of Δh Bivariate Appell Polynomials: An In-Depth Investigation and Extension through Fractional Operators

Exploring the Characteristics of Δh Bivariate Appell Polynomials: An In-Depth Investigation and Extension through Fractional Operators

On new generalized discrete U -Bernoulli-Korobov-kind polynomials and some of their properties

Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials

Contact Info

Product

Resources

About