V.V. Zajtsev - Ph. D. (Phys.-Math.), Professor, Department of Radiophysics, Samara State University. E-mail: zaitsev@ssu.samara.ru Ar.V. Karlov - Post-graduate Student, Department of Radiophysics, Samara State University. E-mail: ar.karlov@gmail.com I.V. Stulov - Post-graduate Student, Department of Radiophysics, Samara State University. E-mail: stulov.i.v@mail.ru

A mathematical model of self-oscillating system with differential equation of fractional order is introduced to consideration on an example of Thomson type oscillator with fractal excitation circuit of oscillating loop. Analysis of the model is performed by the methods of equivalent linearization and slowly varying amplitudes. The characteristics of steady self-oscillations mode are defined. A system of linearized fluctuation equations, that describes the fluctuations of amplitude and frequency of steady self-oscillation at presence of broadband noise source in self-oscillator is obtained. The spectral characteristics of fluctuations of amplitude and frequency of self-oscillation are defined. It is shown that introduction of fractional bonds in the oscillating system degrades its noise characteristics.

 

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