Abstract:

The article deals with a number of application models that lead to the use of the apparatus of continued fractions, and the algorithms for the obtained models. This is, in particular, the model of the mechanism of genetic control, the model of the mechanism of infectious disease, the task of optimal regulation and proposes approximate methods for the expansion of nonlinear integral equations by continued fractions operator. To understand nonlinear aspects of reality in the scientific method, i t can be used a description of such non-linearity, including using nonlinear equations of differential and integral equations. To solve such equations can be used as state-dependent Riccati equation (SDRE) as periodic function to study interactions. This work discuss continuous fractions operator (OCF) to solving non-linear integral equations. That approach can be used in iterative procedures and in engineering software packages. General nonlinear equation can be express by continuous fractions operator (OCF), and subset of it - equation of Low type – by periodic OCF. Then the operator of branched continued fractions (OBCF) can be used for more general nonlinear integral equation. Considering the indicated signs of convergence of OBCF indicate the ability to calculate solution of non-linear integral equations with the given accuracy based on the given inequality checking.