Investigation of the kinetic equation of cascade fragmentation theory at not self-similar subdivision

The cascade kinetic fragmentation process of solids is investigated when the condition probability density of splinter formation do not depends on time and has the property $P(\rho ,r,t)=P(\rho \mathrm{/}r)$. It is obtained the evolution equation for the probability distribution density in terms of its Mellin transformation. In the particular case $P(\rho \mathrm{/}r)=C(\rho \mathrm{/}r{)}^{\alpha }$, the limit solution of this equation at $t\to \mathrm{\infty }$ is found. It differs essentially from the Kolmogorov law.