Unraveling multivariable Hermite-Apostol-type Frobenius-Genocchi polynomials via fractional operators

Abstract

This study explores the evolution and application of integral transformations, initially rooted in mathematical physics but now widely employed across diverse mathematical disciplines. Integral transformations offer a comprehensive framework comprising recurrence relations, generating expressions, operational formalism, and special functions, enabling the construction and analysis of specialized polynomials. Specifically, the research investigates a novel extended family of Frobenius-Genocchi polynomials of the Hermite-Apostol-type, incorporating multivariable variables defined through fractional operators. It introduces an operational rule for this generalized family, establishes a generating connection, and derives recurring relations. Moreover, the study highlights the practical applications of this generalized family, demonstrating its potential to provide solutions for specific scenarios.

Keywords

• operational connection
• fractional operators
• eulers' integral
• multivariable special polynomials
• explicit form
• applications