Research Article
Year 2023,
, 143 - 147, 26.03.2023
Abstract
Supporting Institution
FIRAT ÜNİVERSİTESİ
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References
- [1] Nishimoto K., An essence of Nishimoto's Fractional Calculus (Calculus in the 21st century): Integrations and Differentiations of Arbitrary Order, Descartes Press Company, Koriyama, (1991).
- [2] Weilber M., Efficient Numerical Methods for Fractional Differential Equations and their Analytical Background, Ph. D. Thesis, Von der Carl-Friedrich-Gaub-Fakultur Mathematic and Informatik der Te chnis-chen University, 2005.
- [3] Khalil, R., Al Harani, M., Yousef A., Sababheh M., A new definition of fractional derivative, J. Comput and Applied Mathematics, 264 (2014) 65-70.
- [4] Baleanu, D., Vacaru, S., Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics, Open Physics, 9(5) (2011) 1267-1279.
- [5] Baleanu, D., Vacaru, S. I., Fractional almost Kähler–Lagrange geometry, Nonlinear Dynamics, 64(4) 365-373.
- [6] Abdeljawad, T., Alzabut, J., Jarad, F., A generalized Lyapunov-type inequality in the frame of conformable derivatives, Advances in Difference Equations, 2017(1) 1-10.
- [7] Abdeljawad, T., Agarwal, R. P., Alzabut, J., Jarad, F., Özbekler, A., Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives, Journal of Inequalities and Applications, 1 (2018) 1-17.
- [8] Atangana, A., Baleanu, D., Alsaedi, A., New properties of conformable derivative, Open Mathematics, 13(1) (2015).
- [9] Anderson, D. R., Ulness, D. J., Newly Defined Comformable Derivatives Centered Polygonal Lacunary Functions View project Dynamic Equations on Times Scales View Project Newly Defined Comformable Derivatives, Advances in Dynamical Systems and Applications, 10(2) (2015) 109-137.
- [10] Aminikhah H., Sheikhani A.H.R., Rezazadeh H., Sub-equation method fort he fractional regularized long-wave equations with comformable fractional derivatives, Sci. Iran, 23 (2016) 1048-1054.
- [11] Gözütok U., Çoban H., Sağıroğlu Y., Frenet frame with respect to conformable derivative, Filomat., 33 (6) (2019).
- [12] Mağden A., Yılmaz S., Ünlütürk Y., Characterizations of special time-like curves in Lorentzian plane , International Journal of Geometric Methods In Modern Physics., 14 (10) (2017).
Year 2023,
, 143 - 147, 26.03.2023
Abstract
In this paper, we get some characterizations of conformable curve in R^2. We investigate the conformable curve in R^2. We define the tangent vector of the curve using the conformable derivative and the arc parameter s. Then, we get the Frenet formulas with conformable frames. Moreover, we define the location vector of conformable curve according to Frenet frame in the plane R^2.
Finally, we obtain the differential equation characterizing location vector and curvature of conformable curve in the plane R^2.
References
- [1] Nishimoto K., An essence of Nishimoto's Fractional Calculus (Calculus in the 21st century): Integrations and Differentiations of Arbitrary Order, Descartes Press Company, Koriyama, (1991).
- [2] Weilber M., Efficient Numerical Methods for Fractional Differential Equations and their Analytical Background, Ph. D. Thesis, Von der Carl-Friedrich-Gaub-Fakultur Mathematic and Informatik der Te chnis-chen University, 2005.
- [3] Khalil, R., Al Harani, M., Yousef A., Sababheh M., A new definition of fractional derivative, J. Comput and Applied Mathematics, 264 (2014) 65-70.
- [4] Baleanu, D., Vacaru, S., Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics, Open Physics, 9(5) (2011) 1267-1279.
- [5] Baleanu, D., Vacaru, S. I., Fractional almost Kähler–Lagrange geometry, Nonlinear Dynamics, 64(4) 365-373.
- [6] Abdeljawad, T., Alzabut, J., Jarad, F., A generalized Lyapunov-type inequality in the frame of conformable derivatives, Advances in Difference Equations, 2017(1) 1-10.
- [7] Abdeljawad, T., Agarwal, R. P., Alzabut, J., Jarad, F., Özbekler, A., Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives, Journal of Inequalities and Applications, 1 (2018) 1-17.
- [8] Atangana, A., Baleanu, D., Alsaedi, A., New properties of conformable derivative, Open Mathematics, 13(1) (2015).
- [9] Anderson, D. R., Ulness, D. J., Newly Defined Comformable Derivatives Centered Polygonal Lacunary Functions View project Dynamic Equations on Times Scales View Project Newly Defined Comformable Derivatives, Advances in Dynamical Systems and Applications, 10(2) (2015) 109-137.
- [10] Aminikhah H., Sheikhani A.H.R., Rezazadeh H., Sub-equation method fort he fractional regularized long-wave equations with comformable fractional derivatives, Sci. Iran, 23 (2016) 1048-1054.
- [11] Gözütok U., Çoban H., Sağıroğlu Y., Frenet frame with respect to conformable derivative, Filomat., 33 (6) (2019).
- [12] Mağden A., Yılmaz S., Ünlütürk Y., Characterizations of special time-like curves in Lorentzian plane , International Journal of Geometric Methods In Modern Physics., 14 (10) (2017).
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | March 26, 2023 |
| Submission Date | March 2, 2022 |
| Acceptance Date | December 19, 2022 |
| Published in Issue | Year 2023 |