This study analyses (k,m)-type slant helices in compliance with the modified orthogonal frame in 3-dimensional Euclidean space ($\mathbb{E}^{3}$). Furthermore, we perform some characterisations of curves with modified orthogonal frames in $\mathbb{E}^{3}$.

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.