In this paper we show that the compensation of loss in the linear fractional oscillator by an active device can result in auto-oscillations. Due to the main feature of linear fractional oscillations, namely a finite number of zeros, the limit cycle in such a generator has a short life time depending on the order of fractional derivative. The electronic circuit, leading to such auto-oscillations, is studied as an example, and its differential equation is derived. The active device characteristic is represented in the piecewise-linear approximation. The features of electric elements are discussed.

PACS numbers: 05.45.--a, 05.40.Fb, 07.50.--e