In this paper, we define a new generalization of Laguerre-based Appell polynomials with two parameters. We obtain a recurrence relation, a lowering operator, a integro-partial raising operator, a integro-partial differential equation for this new polynomial family. We introduce subpolynomials of these polynomials, namely Laguerre-based Hermite-Frobenius Euler polynomials, Laguerre-based Miller-Lee polynomials and generalizations of Laguerre-based Hermite polynomials and obtain various properties of them. We also show 3D graphs of these subfamilies and graphs of the distribution of their real roots.
Hepsisler et al. (Wed,) studied this question.