Bisector Curves of Comformable Curves in R^2 - Özel, Şeyda; Bektaş, Mehmet (My University, 2025)
In this study, initially, information about the derivative of fractional order was given. Subsequently, one of the fractional derivative types, namely the comformable derivative was discussed in detail. Additionally, the studies conducted on this comformable derivative type were also included. The importance of the bisector structure on the theory of curves was mentioned. In the second part of the study, the materials and methods were demonstrated using the comformable derivative. Finally, in this work, the bisector curves of two regular comformable curves from C^1-regular parametric category is inspected in R^2. Then, multivariable functions which are corresponded to bisector curves of regular comformable curves are calculated. The bisector curves are procured by two similar paths. The methods of finding this function were demonstrated in detail using comformable derivatives. Then, the equations which are corresponded to bisector curves are obtained in R^2.
Keywords: Bisector curve; Comformable derivative; Frenet drame