A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators

Mohra Zayed; Shahid Ahmad Wani; Georgia Irina Oros; William Ramŕez; Mohra Zayed; Shahid Ahmad Wani; Georgia Irina Oros; William Ramŕez

doi:10.3934/math.2024789

AIMS Mathematics

2024, Volume 9, Issue 6: 16297-16312. doi: 10.3934/math.2024789

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A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators

1.
Mathematics Department, College of Science, King Khalid University, Abha, 61413, Saudi Arabia
2.
Symbiosis Institute of Technology, Symbiosis International (Deemed) University (SIU), Pune, Maharashtra, India
3.
Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, Oradea 410087, Romania
4.
Section of Mathematics International Telematic University Uninettuno, Rome 00186, Italy
5.
Department of Natural and Exact Sciences, Universidad de la Costa, Barranquilla 080002, Colombia

Received: 24 February 2024 Revised: 22 April 2024 Accepted: 28 April 2024 Published: 09 May 2024
MSC : 33E20, 33C45, 33B10, 33E30, 11T23

Originally developed within the realm of mathematical physics, integral transformations have transcended their origins and now find wide application across various mathematical domains. Among these applications, the construction and analysis of special polynomials benefit significantly from the elucidation of generating expressions, operational principles, and other distinctive properties. This study delves into a pioneering exploration of an extended lineage of Frobenius-Euler polynomials belonging to the Hermite-Apostol type, incorporating multivariable variables through fractional operators. Motivated by the exigencies of contemporary engineering challenges, the research endeavors to uncover the operational rules and establishing connections inherent within these extended polynomials. In doing so, it seeks to chart a course towards harnessing these mathematical constructs within diverse engineering contexts, where their unique attributes hold the potential for yielding profound insights. The study deduces operational rules for this generalized family, facilitating the establishment of generating connections and the identification of recurrence relations. Furthermore, it showcases compelling applications, demonstrating how these derived polynomials may offer meaningful solutions within specific engineering scenarios.
- fractional operators,
- Eulers' integral,
- multivariable special polynomials,
- explicit form,
- operational connection,
- applications
Citation: Mohra Zayed, Shahid Ahmad Wani, Georgia Irina Oros, William Ramŕez. A study on extended form of multivariable Hermite-Apostol type Frobenius-Euler polynomials via fractional operators[J]. AIMS Mathematics, 2024, 9(6): 16297-16312. doi: 10.3934/math.2024789

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Abstract

Originally developed within the realm of mathematical physics, integral transformations have transcended their origins and now find wide application across various mathematical domains. Among these applications, the construction and analysis of special polynomials benefit significantly from the elucidation of generating expressions, operational principles, and other distinctive properties. This study delves into a pioneering exploration of an extended lineage of Frobenius-Euler polynomials belonging to the Hermite-Apostol type, incorporating multivariable variables through fractional operators. Motivated by the exigencies of contemporary engineering challenges, the research endeavors to uncover the operational rules and establishing connections inherent within these extended polynomials. In doing so, it seeks to chart a course towards harnessing these mathematical constructs within diverse engineering contexts, where their unique attributes hold the potential for yielding profound insights. The study deduces operational rules for this generalized family, facilitating the establishment of generating connections and the identification of recurrence relations. Furthermore, it showcases compelling applications, demonstrating how these derived polynomials may offer meaningful solutions within specific engineering scenarios.

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