This is the launchpoint for the book _Calculus in a New Key_ by D. L. Orth. It sure SOUNDS interesting, but the noninteger derivative doesn't simplify anything I've ever worked on.
If you want to do it with the Excel Fourier transform tool:
get the new phase angle from the derivative order, nu
get the real and imaginary parts from the new phase angle and the absolute value of the transform and the sign of the original real and imaginary parts.
multiply the phase adjusted real and imaginary by the frequency^nu
I do not know the purpose and use of 'your' fractional derivative. to sum up (d/dy)^r o exp(ay) = a^r*exp(ay) (d/dy)^r o y^n = Gamma(n+1)/Gamma(n-r+1)*y^(n-r) We may also directly build a function g(x,y) such as g(x+r,y) = d/dy)^r o g(x,y) Example g(x,y) = d/dy)^x o (exp(2y)+exp(3y) g(x,y) = 2^x*exp(2y)+3^x*exp(3y) ,
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