Affiliation:
1. FIRAT ÜNİVERSİTESİ, FEN FAKÜLTESİ
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.
Reference12 articles.
1. [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. [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. [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. [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. [5] Baleanu, D., Vacaru, S. I., Fractional almost Kähler–Lagrange geometry, Nonlinear Dynamics, 64(4) 365-373.