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)=x lambda 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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Robert M. Ziff (1991) studied this question.
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