fractional derivatives and integrals?



On 03/15/2010 04:40 PM, Janek Kozicki wrote:

> So R-L integral is a function which takes another function as an
> input. So, based on my currently limited knowledge I am doing it this
> way:
>
> 1st define some function which  I want to analyse:
>
> (%i1) fx(x):=x^2;

Often in maxima we work with expressions rather than functions. Your 
R_L_integral could take an expression rather than the name of a 
function. In some sense this is a matter of choice.

> Then I want to plot this function, for alfa=0.5, so first I define it:
>
> (%i3) F(x):=Riemann_Liouville_fractional_integral_left_sided(fx,0,0.5);

I don't think this is doing what you want. This defines the function 
F(x) as a call to another function... Riemann_Liouville etc. I think it 
makes much more sense to evaluate that integral once, and use the result 
as the definition for F. You can do this as follows:

define('F(x), Riemann_...(fx,0,0.5));

This will prevent the Riemann integral from being recalculated every 
time F(x) is evaluated.