Аннотация
In this work, a computational algorithm for determining the fractional order in oscillating systems with liquid dampers occurring in sucker rod pump units is presented. The study particularly focuses on cases where the liquid mass inside the cylinder is sufficiently large, as typically observed in such pumping systems used in oil extraction. These systems exhibit complex dynamic behavior due to the interaction between the rod string and the fluid column. The proposed algorithm provides a more accurate representation of the fractional damping effect and can be effectively applied to improve the modeling, analysis, and optimization of sucker rod pump installations. An asymptotic method is introduced to solve the problem by introducing the inverse value of the mass as a small parameter. At this time, the obtained equation is reduced to the Volterra integral equation of the second kind with respect to the second order derivative of the phase coordinate. Then, an asymptotic separation is introduced to solve the equation. This separation is taken into account in the obtained Volterra integral equation and integrated twice, as a result, the solution of the equation is obtained. A quadratic functional is constructed using statistical data. The obtained solution and statistical data are taken into account in the quadratic functional. Using the least squares method, we ensure that the theoretical results coincide with the statistical data, and as a result, a more efficient fractional order is determined. Then, a calculation algorithm is proposed. Since some steps of this algorithm need explanation, the issue of the implementation of the algorithm is considered. Keywords: fractional order; oscillatory system; liquid damper; asymptotic method; Volterra integral equation; least squares method.