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Fractionalderivative.gif (360 × 222 pixels, file size: 340 KB, MIME type: image/gif, looped, 101 frames)

Summary

Description
English: Fractional derivative of a Gaussian (following Euler's definition) for orders from zero to one.
Date
Source https://twitter.com/j_bertolotti/status/1030403517641568256
Author Jacopo Bertolotti
Permission
(Reusing this file)
https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 11.0 code

plots = Table[
   Plot[
    Sum[an[[j + 1]] Gamma[j + 1]/Gamma[j + 1 - \[Alpha]] (x)^(
      j - \[Alpha]), {j, Ceiling[\[Alpha]], nn}]
    , {x, 0.2, 3.8}, PlotRange -> {-1.5, 1.5}, Ticks -> None, 
    Axes -> {True, False}, PlotStyle -> {Thick, Blue}, 
    Epilog -> {Text[
       StringForm[
        "\!\(\*FractionBox[\(\*SuperscriptBox[\(\[PartialD]\), \
\(``\)]\*SuperscriptBox[\(e\), \(-\*SuperscriptBox[\(x\), \
\(2\)]\)]\), \(\[PartialD]\*SuperscriptBox[\(x\), \(``\)]\)]\)", \
\[Alpha], \[Alpha]], {0.5, 1}]}]
   , {\[Alpha], 0, 1, 0.01}];
Export["<path>/fractionalderivative.gif", plots]

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

This file, which was originally posted to https://twitter.com/j_bertolotti/status/1030403517641568256, was reviewed on 19 October 2018 by reviewer Ronhjones, who confirmed that it was available there under the stated license on that date.

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17 August 2018

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Date/TimeThumbnailDimensionsUserComment
current13:58, 20 August 2018Thumbnail for version as of 13:58, 20 August 2018360 × 222 (340 KB)BertoUser created page with UploadWizard

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