FRACTIONAL DUFFING'S EQUATION AND GEOMETRICAL RESONANCE

We investigate the Fractional Duffing equation in the presence of nonharmonic external perturbations. We have applied the concept of Geometrical Resonance to this equation. We have obtained the conditions that should be satisfied by the external driving forces in order to produce high-amplitude periodic oscillations avoiding chaos. We also show that, for Duffing's equation with fractional damping, the perturbations that satisfy the Geometrical Resonance conditions are nonperiodic functions.