Fractional Hermite-Kampé de Fériet and related polynomials

D. Caratelli, P. E. Ricci

The goal of this paper is to demonstrate that incorporating the fractional form of the exponential function allows for an extension of special polynomials, such as the Hermite-Kampé de Fériet (H-KdF) polynomials with two variables, and the Mittag-Leffler-Gould-Hopper polynomials. This extension can be achieved by defining expansions using fractional powers, while still preserving the essential properties of the corresponding polynomial versions. Specifically, a fractional version of the classical Hermite polynomials is derived. The main properties are based on expansions in integer powers. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(1) (2024), pp. 11-19