  Fractional derivative in time variable is introduced into the Fokker-Planck
equation of a population growth model. It's solution, the KNO scaling function,
is transformed into the generating function for the multiplicity distribution.
Formulas of the factorial moment and the $H_j$ moment are derived from the
generating function, which reduces to that of the negative binomial
distribution (NBD), if the fractional derivative is replaced to the ordinary
one. In our approach, oscillation of $H_j$ moment appears contrary to the case
of the NBD. Calculated $H_j$ moments are compared with those given from the
data in $p\bar{p}$ collisions and in $e^+e^-$ collisions.
