Cosmological models in the theory of fractional action functional

The objective of the work is to obtain and study the dynamical equations for cosmological models based on the effective action of fractional order. In order to derive the modified Friedmann equations of the homogeneous and isotropic cosmological models phenomenologically constructed on the basis of fractional action, the author applies generalization of the Euler-Poisson equation obtained previously in the theory of fractional functional. To obtain exact solutions the researchers uses mathematical ansätzs and phenomenological laws of the cosmological term evolution. The dynamical equations and their exact solutions in the cosmological theory of the fractional action are obtained. The article considers two types of cosmological models: the model of fractional total action functional and the fractional model of the Einstein – Hilbert action. The study investigates the cases of various equations of state of the matter that fills the universe. On the basis of some ansatzs for the cosmological term proposed in this paper, exact solutions to the dynamical equations of the models are obtained. Some examples of the laws of evolution of the cosmological term, widely discussed in the literature, are provided. The author also establishes the possibility of accelerated expansion of the universe in his models. The results demonstrate the new features of cosmological models derived from the fractional action compared to the standard models and open up new possibilities in the study of the dark energy phenomenon. The expected fields of application of the obtained results are the theoretical cosmology and astrophysics.