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

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.