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This paper is devoted to description of the long time time asymptotics of  two critical cases of these equations, when the division rate is constant and the growth rate is  linear or zero. The study of these cases may be reduced to the study of the following fragmentation equation:$$\\frac{\\partial}{\\partial t} u(t,x)  +  u(t,x)=\\int\\limits\\_x^\\infty k\\_0(\\frac{x}{y})  u(t,y) dy.$$Using the Mellin transform of the equation, we determine the long time behavior of the solutions. 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