Abstract
Abstract
This paper introduces a new family of multivariate Hermite-based Appell polynomials with a one-parameter extension, defined through an appropriate generating function. Explicit series representations, operational formulas, and a fractional integral representation are established, revealing their underlying algebraic structure. A determinant representation is derived, providing an effective characterization of the proposed polynomials. Moreover, several families of ordinary, integrodifferential, and partial differential equations satisfied by these polynomials are obtained via operational and factorization techniques. Various summation identities are also presented, enhancing their analytical and computational applicability. As notable special cases, the corresponding results for multivariate Hermite-based Bernoulli, Euler, and Genocchi polynomials are derived, demonstrating that the proposed framework unifies and generalizes several classical Appell-type polynomial families.