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Response characteristics of a fractional oscillator. (English) Zbl 0995.70017
Summary: The integral equation of motion of a driven fractional oscillator is obtained by generalizing the corresponding equation of motion of a driven harmonic oscillator to include integrals of arbitrary order according to the methods of fractional calculus. The Green’s function solution for the fractional oscillator is obtained in terms of Mittag-Leffler functions using Laplace transforms. The response and resonance characteristics of the fractional oscillator are studied for several cases of forcing function.
MSC:
70J35Forced linear oscillatory motions