### 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}

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