Abstract: In the paper we submit the non-local modification of
kinetic Smoluchowski equation for binary aggregation applying to
dispersed media having memory. Our supposition consists in that that
intensity of evolution of clusters is supposed to be a function of the
product of concentrations of the lowest orders clusters at different
moments. The new form of kinetic equation for aggregation is
derived on the base of the transfer kernels approach. This approach
allows considering the influence of relaxation times hierarchy on
kinetics of aggregation process in media with memory.