REALIZATION ALGORITHM FOR DEFINING FRACTIONAL ORDER IN OSCILLATING SYSTEMS WITH LIQUID MPER

REALIZATION ALGORITHM FOR DEFINING FRACTIONAL ORDER IN OSCILLATING SYSTEMS WITH LIQUID MPER

N.S. Hajiiyeva, I.V. Aliyeva, F.A. Aliyev

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Abstract

In the paper the problem of defining the fractional order in oscillating systems with liquid damper. Firstly, the equation of the object is reduced to the Volterra integral equation of the second kind with respect to the second order derivative of the phase coordinate. Based on the statistical data the quadratic functional has been constructed. Using the method of successive approximations the obtained Volterra integral equation has been solved and its solution has the form of the Neumann series. By means of the least squares method, we ensure that the theoretical results coincide with the statistical data, and as a result, a more effective fractional order is determined. Then, an effective algorithm is proposed. Since some steps of this algorithm need explanation, the issue of the implementation of the algorithm is considered.

Keywords

fractional order differential equations, the least squares method, statistical data.