Abstract
The new algebraic properties of the parametric Apostol-type Frobenius-Euler polynomials and parametric type Frobenius-Euler polynomial have been explained in this research. The researchers have studied the series of the Taylor type and established the relation between the classic Apostol Frobenius-Euler and Frobenius-Euler polynomials. This work has also addressed the generalized parametric Apostol-type Frobenius-Euler polynomials matrices and has shown some of their properties. Finally, this research provided some factorizations of Apostol-type Frobenius-Euler matrix that involves the generalized Pascal matrix, Fibonacci and Lucas matrices, respectively.
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