About properties and the monomiality principle of Bell-based Apostol-Bernoulli-type polynomials

This article investigates the properties and monomiality principle within Bell-based Apostol-Bernoulli-type polynomials. Beginning with the establishment of a generating function, the studyproceeds to derive explicit expressions for these polynomials, providing insight into their structuralcharacteristics. Summation formulae are then derived, facilitating efficient computation and ma-nipulation. Implicit formulae are also examined, revealing underlying patterns and relationships.Through the lens of the monomiality principle, connectionsbetween various polynomial aspects areelucidated, uncovering hidden symmetries and algebraic properties. Moreover, connection formu-lae are derived, enabling seamless transitions between different polynomial representations. Thisanalysis contributes to a comprehensive understanding of Bell-based Apostol-Bernoulli-type poly-nomi.als, offering valuable insights into their mathematical nature and applications