Asymptotical method for solution of identification problem defining the fractional order in oscillatory systems with liquid dampers

In this work, when the mass inside the plunger in the oscillating system is large enough, 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.