Fractional order operational calculus and extended Hermite-Apostol type Frobenius-Euler polynomials

Abstract

The combined use of integral transforms and special classes of polynomials provides a powerful tool to deal with models based on fractional order derivatives. In this article, the operational representations for the extended Hermite-Apostol type Frobenius-Euler polynomials are introduced via integral transforms. The recurrence relations and some identities involving these polynomials are established. Finally, the quasi-monomial properties for the Hermite-Apostol type Frobenius-Euler polynomials and for their extended forms are derived.