Yağmur, Tülay2025-01-152025-01-1520241304-7981https:/dx.doi.org/10.54187/jnrs.1447678https://hdl.handle.net/20.500.12451/12727In the present paper, we introduce a new type of Pell and Pell-Lucas numbers in terms of non-Newtonian calculus, which we call non-Newtonian Pell and non-Newtonian Pell-Lucas numbers, respectively. In non-Newtonian calculus, we study some significant identities and formulas for classical Pell and Pell-Lucas numbers. Therefore, we derive some relations with non-Newtonian Pell and Pell-Lucas numbers. Furthermore, we investigate some properties of non-Newtonian Pell and Pell-Lucas numbers, including Catalan-like identities, Cassini-like identities, Binet-like formulas, and generating functions.eninfo:eu-repo/semantics/openAccessNon-Newtonian CalculusPell NumberPell-Lucas NumberArticle131223510.54187/jnrs.1447678