- #1
eljose
- 492
- 0
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]
[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]
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