On the Characterization of Smarandache Curves of Fractional Order in Euclidean 3-Space

This paper investigates and characterizes Smarandache space curves, an important class of curves, using the Caputo fractional Frenet frame. The Frenet frame and fractional curvature functions have been calculated for these fractional Smarandache curves. To demonstrate the theoretical results obtained, an example of a fractional Smarandache curve derived from a helical curve is considered, and the curvatures of this curve are explicitly calculated. Finally, to show the effect of the fractional order parameter on the geometric behavior, a graphical analysis of the curvatures obtained for different fractional orders is presented.