In this paper we are interested in two-dimensions fragmentation process that describes the evolution of an object having a rectangular shape. We focus on the non-homogenous fragmentation process where we break a rectangle according to a distribution that depends on its dimensions. Via Integral equations tools, we compute the mean and the variance of the distribution of the total number of the sub-rectangles obtained at the end of the process.

In this paper we investigate the size of a bi-dimensional fragmentation process. A rectangle of dimensions x and y is considered, it is split into four sub-rectangles with some probability that depends on x and y, we iterate until the stop of the process. The total number of the all the obtained rectangles at the end of the process satisfies some equality in distribution which is resolved , using some tools on integral equations, via the contraction method.