# problem with a fractional derivative

I want to evaluate the half derivative function of $1/t$

by induction i get that for every 's' then $D_{x}^{s} \frac{1}{t}=\frac{\Gamma(s+1)(-1)^{s}}{t^{s+1}}$

however if i use the formulae from mathworld i get $D_{x}^{s}\frac{1}{t}=\frac{\Gamma (0)}{t^{s+1}}$

which is a nonsense since $\Gamma (0) = \infty$

then which formula is correct ? , also for real 's' can i use $(-1)^{s}=cos(\pi s)$

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S=1/2 so gamma is... and check your generalized power rule. –  user60675 Sep 6 '13 at 20:10