Abstract
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.
References
- Anderson DR, Ulness DJ. 2015. Newly defined conformable derivatives. Adv Dyn Syst Appl, 10(2): 109-137.
- Atangana A, Baleanu D, Alsaedi A. 2015. New properties of conformable derivative. Open Math, 13(1): 889-898.
- Dede M, Ünlütürk Ekici C. 2013. Bisector curves of planar rational curves in Lorentzian plane. Inter J Geo, 2(1): 47-53.
- Elber G, Kim MS. 1998. The bisector surface of rational space curves. ACM Transact Graph, 17(1): 32-49.
- Farouki RT, Johnstone JK. 1994. The bisector of a point and a plane parametric curve. Comput Aided Geom Desig, 11(2): 117-151.
- Gözütok U, Çoban H, Sağıroğlu Y. 2019. Frenet frame with respect to conformable derivative. Filomat, 33(6): 1541-1550.
- Gür Mazlum S, Bektaş M. 2022. On the modified orthogonal frames of the non-unit speed curves in Euclidean 3-space E^3. Turkish J Sci, 7(2): 58-74.
- Gür Mazlum S, Bektaş M. 2023. Involüte curves of any non-unit speed curve in Euclidean 3-space E^3. In: Akgül H, Baba H, İyit N, editors. In international studies in Science and Mathematics. Serüve Publishing, Ankara, Türkiye, pp: 177-195.
- Gür Mazlum S. 2024. On Bishop frames of any regular curve in Euclidean 3- space E^3. Afyon Kocatepe Univ J Sci Engin, 24(1): 23-33.
- Has A, Yılmaz B, Akkurt A, Yıldırım H. 2022. Comformable special curves in Euclidean 3-space E^3. Filomat, 36(14): 4687-4698.
- Khalil R, Al Horani M, Yousef A, Sababheh M. 2014. A new definition of fractional derivative. J Comput Appl Math, 264: 65-70.
- Nishimoto K. 1991. Essence of Nishimoto’s fractional calculus (Calculus of the 21st Century). Integrals and Differentiations of Arbitrary order, Descartes Press, Koriyama, Japan, pp: 208.
Abstract
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.
References
- Anderson DR, Ulness DJ. 2015. Newly defined conformable derivatives. Adv Dyn Syst Appl, 10(2): 109-137.
- Atangana A, Baleanu D, Alsaedi A. 2015. New properties of conformable derivative. Open Math, 13(1): 889-898.
- Dede M, Ünlütürk Ekici C. 2013. Bisector curves of planar rational curves in Lorentzian plane. Inter J Geo, 2(1): 47-53.
- Elber G, Kim MS. 1998. The bisector surface of rational space curves. ACM Transact Graph, 17(1): 32-49.
- Farouki RT, Johnstone JK. 1994. The bisector of a point and a plane parametric curve. Comput Aided Geom Desig, 11(2): 117-151.
- Gözütok U, Çoban H, Sağıroğlu Y. 2019. Frenet frame with respect to conformable derivative. Filomat, 33(6): 1541-1550.
- Gür Mazlum S, Bektaş M. 2022. On the modified orthogonal frames of the non-unit speed curves in Euclidean 3-space E^3. Turkish J Sci, 7(2): 58-74.
- Gür Mazlum S, Bektaş M. 2023. Involüte curves of any non-unit speed curve in Euclidean 3-space E^3. In: Akgül H, Baba H, İyit N, editors. In international studies in Science and Mathematics. Serüve Publishing, Ankara, Türkiye, pp: 177-195.
- Gür Mazlum S. 2024. On Bishop frames of any regular curve in Euclidean 3- space E^3. Afyon Kocatepe Univ J Sci Engin, 24(1): 23-33.
- Has A, Yılmaz B, Akkurt A, Yıldırım H. 2022. Comformable special curves in Euclidean 3-space E^3. Filomat, 36(14): 4687-4698.
- Khalil R, Al Horani M, Yousef A, Sababheh M. 2014. A new definition of fractional derivative. J Comput Appl Math, 264: 65-70.
- Nishimoto K. 1991. Essence of Nishimoto’s fractional calculus (Calculus of the 21st Century). Integrals and Differentiations of Arbitrary order, Descartes Press, Koriyama, Japan, pp: 208.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | January 15, 2025 |
| Submission Date | September 14, 2024 |
| Acceptance Date | November 26, 2024 |
| Published in Issue | Year 2025 |