# Fractional derivative ?

1. Mar 12, 2005

### eljose

from the expression for a Fractional integral of arbitrary order:

$$D^{-r}=\frac{1}{\Gamma(r)}\int_c^xf(t)(x-t)^{r-1}$$

if we set r=-p then we would have for the Fractional derivative:

$$D^{p}=\frac{1}{\Gamma(-p)}\int_c^xf(t)(x-t)^{-(p+1)}$$

is my definition correct?..i mean if its correct to introduce the change of variable r=-p to obtain fractional derivative form fractional integral...

where $$\pi/{\Gamma(-p)}=\Gamma(p+1)sen(p+1)\pi$$

Last edited: Mar 12, 2005
2. Mar 12, 2005

### matt grime

The idea of *a* fractional derivative is well known. If you look over the examples sheets for the first year calculus course at www.maths.bris.ac.uk/~madve[/URL] you'll find it explained on there somewhere I think.

Last edited by a moderator: Apr 21, 2017