Kilar, NeslihanSimsek, Yilmaz2024-11-072024-11-0720232687-4814https://hdl.handle.net/11480/11572The goal of this paper is to define new families of unified and modified presentation of the Fubini numbers and polynomials with their generating functions. Using generating functions and their functional equations, many properties of these polynomials and numbers are presented. Relations among unified and modified presentation of the Fubini numbers and polynomials, Stirling type numbers, combinatorial type polynomials, and unified presentation of the generalized Bernoulli, Euler and Genocchi polynomials are given. Many novel identities and relations including these polynomials and numbers are also given. Moreover, new Hurwitz-Lerch type zeta functions, which interpolate unified and modified presentation of the Fubini numbers and polynomials at negative integers, are defined. Furthermore, suitable links of identities and relations, which are found in this paper, with those in earlier and future studies are indicated. © 2023, MTJPAM Turkey. All rights reserved.eninfo:eu-repo/semantics/closedAccessApostol type numbers and polynomialscombinatorial type numbersFubini type numbers and polynomialsgeneralized Apostol type numbers and polynomialsgenerating functionspecial numbersStirling type numbersArticle511212-s2.0-85163003762N/A