Fractional Derivative Graph of a Quadratic Function

thingiverse

This is a three-dimensional visualization of x^2, featuring one horizontal axis that spans the range of Riemann-Liouville fractional derivative orders 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 clearly highlighted with a prominent ridge. Thanks to its continuous nature with respect to the order of the derivative, the Riemann-Liouville fractional derivative transitions smoothly between the zeroth, first, and second derivatives, as well as the fractional derivatives in between, resulting in a graph that is both intricate and elegant. For a discrete quadratic version, see https://www.thingiverse.com/thing:3786851. See https://www.thingiverse.com/thing:2699923 for another visually striking representation of a fractional derivative graph, this time with an exponential function.