Continuous Fractional Derivative of Quadratic Function


This is a three dimensional graph of \(x^2\), with one axis representing the Riemann-Liouville fractional derivative order ranging from 0 to 2. The \(x\)-axis ranges from 1 to 7. The zeroth order derivative, given by \(x^2\), the first derivative, given by \(2x\), and the second derivative, given by \(2\) 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.

Design process:

I used Mathematica to generate the graph using the included Mathematica code. Then I used Slic3r to scale the Mathematica output to be \(80\times80\times80\) \(\text{mm}^3\) (as well as let it correct some errors in the stl file). Finally, I used Fusion 360 to design the stand.

Post-print finishing:

If desired, use a few drops of super glue to attach the surface to the stand.