  I show a nontrivial functional giving a conservation quantity in the
collisional energy cascade of dissipative Maxwell gases: a fractional-calculus
extension of the mean energy. The conservation of this quantity directly leads
the power-law energy tail that is stationary during the temporal evolution. In
the thermal limit, this quantity naturally reduces to the standard mean energy.
This conservation law and its extension to particles with other interactions
are demonstrated with a Monte-Carlo simulation for inelastic gases.
