Some families of differential equations associated with the multivariable hybrid special polynomials

Abstract In this article, a novel family of multi-variate Hermite-Frobenius-Euler polynomials is constructed and its several characterizations are observed. The properties of these polynomials, such as recurrence relations and shift operators, are investigated. Differential equations, partial differential equations, and integrodifferential equations satisfied by these polynomials are derived using the factorization method. Additionally, the Volterra integral equation is derived for these multi-variate Hermite-Frobenius-Euler polynomials, which enhances the understanding and application of the factorization method in physics and engineering. MSC (2020) : 33E20; 33B10; 45J05; 65Q30; 65R20