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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so... to cos and sin the aᵗʰ derivate is the same as f(x)↦f(x+a)
i don't think the phase change is exactly a.. maybe a*π/2 though..
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I like these fact cause it links translation on fonctions to derivates on functions trough trigonometric polynomials, by the way it is another point of view to maybe see that a closed functiun space under derivation is finite dimensional
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