Fractional Derivative Graph of a Quadratic Function

Описание

This is a three dimensional graph of x^2, with one horizontal axis representing the Riemann-Liouville fractional derivative order ranging from 0 to 2. The other horizontal axis represents x values ranging from 1 to 7. The zeroth order derivative (x^2), the first derivative (2x), and the second derivative (2) are highlighted with a ridge. The Riemann-Liouville fractional derivative is continuous with the respect to the order of the derivative, so the transition between the zeroth, first, and second derivative to the fractional derivatives in between results in a smooth graph. For a discrete quadratic version, see https://www.thingiverse.com/thing:3786851. See https://www.thingiverse.com/thing:2699923 for another fractional derivative graph, this time with an exponential function.