A new perspective on Fibonacci and Lucas numbers

In the present work, we introduce a new version of Fibonacci and Lucas numbers which we will call non-Newtonian Fibonacci and non-Newtonian Lucas numbers. Also, we discuss a variety of some properties of them. Furthermore, we give some formulas and identities such as Binet?s formula, the d?Ocagne?s identity, Cassini?s identity and Gelin-Ces?ro identity involving these new types and we find the generating functions for these numbers.