On the fractional damped oscillators and fractional forced oscillators

摘要

In this paper, we use the fractional calculus to discuss the fractionalmechanics, where the time derivative is replaced with the fractional derivativeof order $\nu$. We deal with the motion of a body in a resisting medium wherethe retarding force is assumed to be proportional to the fractional velocitywhich is obtained by acting the fractional derivative on the position. Thefractional harmonic oscillator problem, fractional damped oscillator problemand fractional forced oscillator problem are also studied.