A study on differential equations associated with ( q , h ) -Frobenius-Euler polynomials

In recent years, utilizing the generalized quantum exponential function (also known as the (q, h)-exponential function) that extends and unifies the qand h-exponential functions into a single and convenient form, (q, h)-generalizations of the diverse polynomials and numbers, such as Euler and tangent polynomials and numbers, have been introduced and studied.Inspired by these studies, in this work, we focus on defining and analyzing extensions of Frobenius-Euler polynomials and numbers using the (q, h)-exponential function.Also, we show that the mentioned polynomials are solutions to some higher-order differential equations.Furthermore, we examine that (q, h)-Frobenius-Euler polynomials are solutions to higher-order differential equations combined with the q-Bernoulli, q-Euler, and q-Genocchi numbers and polynomials, respectively.Finally, we use a computer program to visualize the approximate roots of the mentioned polynomials.