It is possible to write programs to do fractional derivatives, but the
general idea has not caught on, in spite of a substantial history and
I think a (small?) group of enthusiasts. It is a kind of alternative
notation for (some?) special functions. An excellent survey of
results was published in SIAM review, 1976 by Lovoie. It contains many
interesting results, some of which can be immediately inserted into Maxima
(and were the basis of a student project,using Macsyma, at Berkeley,
years ago.)
As I recall there are some glitches that have to be overcome, such as a
disagreement about the definition of some forms, because
consistency between x^n and exp(x) is problematic.
I think it is fair to say that fractional derivatives are not in Maxima
because they haven't been found to be useful, at least yet.
Not that they present any great difficulty.
RJF
Alasdair McAndrew wrote:
> You could use the Riemann-Liouville integral (see
> http://en.wikipedia.org/wiki/Riemann?Liouville_integral).
>
> -Alasdair
>
> On Sun, Mar 14, 2010 at 10:12 PM, Janek Kozicki <janek_listy at wp.pl
> <mailto:janek_listy at wp.pl>> wrote:
>
> Hi,
>
> is it possible to calculate fractional derivatives or integrals? And
> do some fractional calculus in general?
>
> For instance I did:
>
> (%i1) x^2;
> (%i2) diff(%,x,0.5);
> (%i3) plot2d([%], [x,-5,5]);
>
> and I got some errors instead of a plot.
>
> When I explicitly define, a fractional derivative of x^n then it
> "sort of" works, but then, how to push it forward with derivatives of
> anything more complex than x^n ?
>
> (%i1)
> fractional_derivative_of_x_n(x,n,k):=(gamma(k+1)/gamma(k-n+1))*x^(k-n);
>
>
> --
> Janek Kozicki
> http://janek.kozicki.pl/ |
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu <mailto:Maxima at math.utexas.edu>
> http://www.math.utexas.edu/mailman/listinfo/maxima
>
>
>
>
> --
> Blog: http://amca01.wordpress.com
> Web: http://bit.ly/Alasdair
> Facebook: http://www.facebook.com/alasdair.mcandrew
> ------------------------------------------------------------------------
>
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>