Abstract
Binary stars are very common in nature, so their study is very important both for explaining the nature of stars and for studying the formation and evolution of stars. Binary stars are stars united into one system by the force of gravity. The components of such systems rotate around a common center of mass. Depending on their size and the position of their orbits in space, as well as their distance from us, binary stars are studied by different methods. In recent years, the study of class B[e] stars has attracted great interest in order to explain the physical properties and parameters of binary stars. Therefore, B[e] class binary stars (3Pup, MWC728, MWC645, BD+23 3183) were chosen as objects of study in this work. The variety of physical properties of objects in the field of astronomy and the nonlinear dependence of their sizes on their values require fractal analysis. Therefore, hierarchical nonlinear fractal models were used to study binary stars. A universal physical model has been created to describe the properties of binary stars and a hierarchical nonlinear fractal equation has been proposed to study the evolution of binary stars. From theoretical calculations and observational data, the ratios between the power spectra of the main and secondary stars were determined. It is shown that theoretical data obtained with the help of nonlinear fractal laws can be used to describe observational data. It turned out that the fractal structure of stars can be described by the laws of the power spectrum.