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Information × Registration Number 0213U002252, 0109U000117 , R & D reports Title Mathematical modelling of selforganization phenomena in dynamical systems with fractional derivatives. popup.stage_title Head Gafiychuk Vasyl; Datsko Bohdan Josypovych, Registration Date 23-01-2013 Organization Pidstryhach Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine popup.description2 The theory of linear stability for nonlinear evolution systems with ordinary and partial fractional derivatives is developed. The theoretical analysis of possible instabilities in reaction-diffusion systems with derivatives of rational order and obtained conditions for various types of instabilities depending on system parameters and the fractional order derivative is performed. The new types of nonlinear solutions for the basic reaction-diffusion systems with fractional derivatives and new types of limit cycles for fractional systems of ordinary differential equations of classical nonlinearity are obtained. The main types of nonlinear dynamic systems with fractional derivatives are studied. The numerical and semi analytical methods for nonlinear systems for evolutionary equations with spatial and time fractional derivatives are proposed. The self-organization phenomena considered in this thesis are general in nature and can be used to investigate a wide class of nonlinear active systems. Product Description popup.authors Васюник З.І. Гафійчук В.В. Дацко Б.Й Котлярчук Б.К. Мелешко В.В. Павлюк В.С. Панасюк А.В. Савчук О.З. popup.nrat_date 2020-04-02 Close