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Fractional derivative ?

  1. Mar 12, 2005 #1
    from the expression for a Fractional integral of arbitrary order:

    [tex]D^{-r}=\frac{1}{\Gamma(r)}\int_c^xf(t)(x-t)^{r-1}[/tex]

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

    [tex]D^{p}=\frac{1}{\Gamma(-p)}\int_c^xf(t)(x-t)^{-(p+1)}[/tex]

    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 [tex]\pi/{\Gamma(-p)}=\Gamma(p+1)sen(p+1)\pi[/tex]
     
    Last edited: Mar 12, 2005
  2. jcsd
  3. Mar 12, 2005 #2

    matt grime

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    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 you'll find it explained on there somewhere I think.
     
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