Re: Fractional derivatives

From: Timothy Murphy <tim@xxxxxxxxxxxxxxxxxxxxxx>
Date: Thu, 21 Jul 2005 13:13:13 +0100

gsax wrote:

> I read someplace that fractional derivatives can be computed by
> tinkering in the Fourier domain of that function.

Derivation goes over to multiplication by x in the Fourier domain;
as I understand it fractional derivation corresponds to
multiplication by x^c.

> My question is, that not all functions have a Fourier transform (
> Dirichlet conditions)...
> so how do we define their fractional derivatives?

I very much doubt if you could define it in this case.
Note that fractional derivatives are not usually local,
like normal derivatives.
They depend on the behaviour of f(t) for all t.

--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
.

References:
- Fractional derivatives
  - From: gsax

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