On the fractional damped oscillators and fractional forced oscillators

TL;DR

This paper explores fractional calculus applications in mechanics, analyzing fractional harmonic, damped, and forced oscillators to understand their dynamics with fractional derivatives.

Contribution

It introduces fractional derivatives into oscillator models, providing new insights into their behavior under fractional damping and forcing.

Findings

Fractional derivatives model damping more accurately.

New solutions for fractional oscillators are derived.

Fractional oscillators exhibit unique dynamic properties.

Abstract

In this paper, we use the fractional calculus to discuss the 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 which is obtained by acting the fractional derivative on the position. The fractional harmonic oscillator problem, fractional damped oscillator problem and fractional forced oscillator problem are also studied.