Search results for "fractional dérivative"

Fractional half-tangent of a curve described by Iterated Function Systems.

2009

International audience; The deterministic fractal curves and surfaces find many applications in modeling of rough objects. However, these curves and surfaces are nowhere differentiable. Without notion of tangent, we can not determine the relative orientation of two fractal shapes, to join them with a "natural" aspect. Various works proposed a generalization of the concept of derivative by introducing the fractional derivative. In this paper we apply this concept of fractional derivative to the curves described by Iterated Function Systems. We show that if the fractional derivative exists at boundary points of the curve, the direction of the fractional half-tangent is necessarily the eigenve…