On the fractional derivative of a type of self-affine curves

This paper investigates the fractal dimension of the Weyl–Marchaud (W–M) fractional derivative of a type of self-affine curves. We first define the W–M fractional derivative of a general self-affine functions, then calculate the Box dimension of them, finally prove a linear relationship between the order of the W–M fractional derivative and the fractal dimension.