ANALYTICAL SOLUTIONS OF A FRACTIONAL OSCILLATOR BY THE DECOMPOSITION METHOD

The equation of motion of a driven fractional oscillator is obtained from the corresponding equation of motion of a driven harmonic oscillator by replacing the second-order time derivative by a fractional derivative of order α with 1 < α ≤ 2. The fractional derivative is described in the Caputo sense. The application of Adomian decomposition method, developed for differential equations of integer order, is extended to derive analytical solutions of the fractional oscillator. The response characteristics and phase plane representation of the fractional oscillator are studied for several cases. AMS Subject Classification: 26A33

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