On Caputo Fractional Bertrand Curves in $\mathbb{E}^3$ and $\mathbb{E}_1^3$

Abstract

In this work, we examine Bertrand curves in $\mathbb{E}^3$ and $\mathbb{E}_1^3$ by using the Caputo fractional derivative which we call $\alpha$-Bertrand Curves. First, we consider $\alpha$-Bertrand curves in $\mathbb{E}^3$ and we
give a characterization of them. Then, we study $\alpha$-Bertrand curves in $\mathbb{E}_1^3$ and we prove the necessary and sufficient condition for a $\alpha$-Bertrand curves in $\mathbb{E}_1^3$ by considering time like, space like and null curves. We also give the related examples by using Python.
\end{abstract}