Kilar, Neslihan2024-11-072024-11-0720242687-4814https://hdl.handle.net/11480/11570The objective of this paper is to build generating functions for new families of special numbers and polynomials, which are called higher order degenerate Peters-type Simsek numbers and polynomials of the second kind. Using generating function methods, we give both some fundamental properties of these functions with some relations among the higher order degenerate Peters-type Simsek numbers and polynomials of the second kind, the Stirling numbers of the first kind, the higher order degenerate Changhee numbers and polynomials, and the higher order Apostol-type Daehee numbers and polynomials. We also give some plots of these numbers and polynomials via Wolfram Cloud. Further, applying a partial derivative operator to these generating functions, we obtain derivative formulas for these new families. Eventually, we present further remarks on our new families including their generating functions. © 2024, MTJPAM Turkey. All rights reserved.eninfo:eu-repo/semantics/closedAccessApostol-type Daehee numbers and polynomialsdegenerate Changhee numbers and polynomialsdegenerate Peters-type Simsek numbers and polynomialsgenerating functionsStirling numbersArticle631861982-s2.0-85192862454N/A