Fractional derivative

*To*: mathgroup at smc.vnet.net*Subject*: [mg32185] Fractional derivative*From*: "Sridhar Ramanujam" <ramanuja at usc.edu>*Date*: Fri, 4 Jan 2002 05:04:02 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Dear Mathgroup members, I was trying to find the inverse fourier transform of (2 I Pi f)^0.5 and I tried it with mathematica and I got the following result: (-0.886227+(0.886227)sign(t))/(t^2)^0.75. Obviously, this is a one-sided function of t. My problem is that if I multiply the fourier transform by itself, one should get a function which is (2 I Pi f) - which is satisfied in the frequency domain but not in the time domain. I don't see one-sided infinite support functions convolving to give the derivative of the dirac delta function. If anyone has any suggestions, please pass them on.... Thanks, Sridhar.