The Differential Equations of Conformable Curve in IR^2

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.