On Caputo fractional Bertrand curves in E3 and E31

Tasdemir M., Canfes E., Uzun B.

Filomat, vol.38, no.5, pp.1681-1702, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.2298/fil2405681t
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1681-1702
  • Keywords: Bertrand Curves, Fractional Derivative, Minkowski Space
  • Istanbul Technical University Affiliated: Yes


In this article, we examine Bertrand curves in E3 and E31 by using the Caputo fractional derivative which we call α-Bertrand Curves. First, we consider α-Bertrand curves in E3 and we give a characterization of them. Then, we study α-Bertrand curves in E31 and we prove the necessary and sufficient condition for a α-Bertrand curves in E31 by considering time like, space like and null curves. We also give the related examples by using Python.