In this research, applied to the problem of formation of planetesimals in Sunny protoplanetary cloud, has been developed (considering the concept of fractal properties of dust clusters) evolutionary hydrodynamic model of the formation and growth of fluffy dust aggregates aerodisperse medium of laminar disk. In contrast to a number of classical researches in which the simulation was carried out as part of the 'ordinary' continuum, and often not taken into account multifractional dust component of the protoplanetary cloud and the fractal nature formed in the process of the evolution of dust clusters, it is proposed to consider a set of fluffy dust aggregates as a special type of continuum medium − a fractal medium for which there are points and areas not filled its particles. The hydrodynamic modeling of similar medium (that has non-integer mass dimensionality) is proposed to take place within the fractional integral model (its differential form) with the help of the fractional integrals, when its order is determined by dimensionality of disk medium.

hydrodynamics of fractal media, coagulation processes, protoplanetary disks

Mathematical modelling in actual problems of science and technics