@article{article_1447678, title={Non-Newtonian Pell and Pell-Lucas numbers}, journal={Journal of New Results in Science}, volume={13}, pages={22–35}, year={2024}, DOI={10.54187/jnrs.1447678}, author={Yağmur, Tülay}, keywords={Non-Newtonian calculus, Pell number, Pell-Lucas number}, abstract={In 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.}, number={1}, publisher={Tokat Gaziosmanpasa University}