Evaluate properties of Bell-based Frobenius-Sigmoid polynomials and applications in computer modeling

The main focus of this investigation is the applications of Sigmoid functions. Due to its various uses in physics, engineering, and computer science, we introduce Bell-based Frobenius-Sigmoid polynomials and numbers. With the help of generating functions and their functional equations, we derive some properties of these types of polynomials and numbers. Furthermore, we derive symmetric identities for the Bell-based Frobenius-Sigmoid numbers and polynomials. Lastly, we present graphical representations and analyze the zeros of the Bell-based Frobenius-Sigmoid polynomials utilizing computational methods.