New solutions to the fragmentation equation

A new general class of exact, explicit scaling solutions to the fragmentation equation is given. This class is described by a breakage rate a(x)=xlambda and the daughter distribution function yb(x mod y)=a gamma (xy)gamma -2+(1-a) delta (x/y)delta -2, and includes as special cases all previously-known scaling solutions to the fragmentation equation. For a subset of this class, with gamma = lambda and a= delta /( delta - lambda ), the complete time-dependent solution for a monodisperse initial condition is also given.

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