Differential and Integral Equations for the 3-Variable Hermite-Frobenius-Euler and Frobenius-Genocchi Polynomials

Abstract

The main goal of the present article is to derive some new classes of differential equations including partial and integrodifferential equations for the 3-variable Hermite-Frobenius-Euler and Frobenius-Genocchi polynomials by use of the factorization method. We also perform a further investigation for aforementioned polynomials and derive corresponding homogeneous Volterra integral equations. The differential equations for these families of polynomials contain, as their special cases, the differential equations for some known special polynomials. Moreover, the inclusion of integral equations is a new and recent investigation which adds some extra attention to these polynomials.