Animation of fractional derivative in Mathematica with order of derivative varying

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

• It is not a free coding service. Meet us halfway, see asking guidelines about how to ask a good question.
– Kuba
Commented May 2, 2018 at 7:24
• I understand that, but please if it is possible give me some source, on reading which I am able to learn how to make it
– ShiS
Commented May 2, 2018 at 7:29
• See documentation for Animate, Plot, D and GIF. You can also search around for animation etc. About your edit, if you check the linked guidelines you will see that this question does not fit.
– Kuba
Commented May 2, 2018 at 7:34

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]


• Thanks. I'll surely try to do better as I practice it more. Today was my first time, I had downloaded Mathematica and had to do this difficult problem quickly as I wanted to include it in my presentation to make it look better
– ShiS
Commented May 2, 2018 at 14:14