Fractional damped oscillators and fractional forced oscillators

Abstract

In this paper, we use fractional calculus to discuss fractional mechanics, where the time derivative is replaced with the fractional derivative of order nu. We deal with the motion of a body in a resisting medium where the retarding force is assumed to be proportional to the fractional velocity that is obtained by applying the fractional derivative to the position. The fractional oscillator problem, the fractional oscillator problem with resistance and the fractional forced oscillator problem are also studied.