Animation of fractional derivative in Mathematica with order of derivative varying

Question

I want to make the animation given at the link https://en.wikipedia.org/wiki/File:Fractional_Derivative_of_Basic_Power_Function_(2014).gif using Mathematica. Is it possible to do it. If it is possible, how can it be done? I am a very beginner to Mathematica and know only a few simple things. Please guide me how can it be done
I am not asking for direct answers, but please give me some pointers, text, documentation, etc.

Answer 1

Of course, you can do it always better than it is.

ANIM = Animate[
Plot[{
Labeled[1, Text[Style["y=1", Large, Bold, Red]], 4], 
Labeled[x, Text[Style["y=x", Large, Bold, Blue]], 1], 
Labeled[x^2/2, Text[Style["y=\!\(\*FractionBox[\(1\), \(2\)]\)*x^2", Large, Bold, RGBColor[1, 0, 1]]], 1.8], 
Labeled[Gamma[2]/Gamma[2 - n]*x^(1 - n), Text[Style["frac", Large, Bold, RGBColor[0, 0.8, 0]]], 5*n]},
{x,0, 5}, PlotRange -> {Automatic, {0, 3}}, 
PlotStyle -> {{Red, Thickness[0.01]}, {Blue, 
  Thickness[0.01]}, {RGBColor[1, 0, 1], 
  Thickness[0.01]}, {RGBColor[0, 0.8, 0], 
  Thickness[0.01]}}], {n, -1.01, 1.01, 0.01}, 
  AnimationDirection -> ForwardBackward, AnimationRate -> 0.25]

Export["test.gif", ANIM]

 ANIM2 = Animate[
 Plot[{Labeled[1, Text[Style["y=1", Large, Bold, Red]], 4], 
 Labeled[x, Text[Style["y=x", Large, Bold, Blue]], 1], 
 Labeled[x^2/2, 
 Text[Style["y=\!\(\*FractionBox[\(1\), \(2\)]\)*x^2", Large, 
   Bold, RGBColor[1, 0, 1]]], 1.8], 
 Gamma[2]/Gamma[2 - n]*x^(1 - n)}, {x, 0, 5}, 
PlotRange -> {Automatic, {0, 3}}, 
PlotStyle -> {{Red, Thickness[0.01]}, {Blue, 
  Thickness[0.01]}, {RGBColor[1, 0, 1], 
  Thickness[0.01]}, {RGBColor[0, 0.8, 0], 
  Thickness[0.01]}}], {n, -1.01, 1.01, 0.01}, 
AnimationDirection -> ForwardBackward, AnimationRate -> 0.25,AppearanceElements -> "HideControlsButton"]

 Export["test2.gif", ANIM2]