Visualizing the Fractional Derivatives of sin(x) • We see that the aᵗʰ derivative of sin(x) smoothly transitions between the familiar sin(x) and cos(x) when a∈[0,1]pic.twitter.com/DFBoRs8MmF
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The 0ᵗʰ through 1ˢᵗ fractional derivatives [ i.e. α∈(0,1) ] are actually defined through an integral relation. (note the familiar structure to Cauchy's Integral Formula)pic.twitter.com/FwJSaaWzeL
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Interesting that the Gamma function gets into this
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How cool! Do you have a Facebook page? Probably not as most the best mathematicians and physicists seem to be only on Twitter. (In the old days Google+ also.)
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We already define differentiation in terms of integration on Sobolev spaces, so this just allows us to expand that a bit more.
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