Analytical Solution of Linear Fractionally Damped Oscillator by Elzaki Transformed Method

Abstract

In this manuscript, linearly and fractionally damped oscillator equation is solved with the help of Caputo fractional derivatives. For 0 ≤ α ≤ 1 oscillation equations change from undamped to damped, whereas α represents the order of Caputo derivative. Analytical solution of nine different cases of critically damped, over-damped and undamped differential equations is found by Elzaki transformation. The oscillatory frequency of three cases of differential equation rises with the increase in damping order before falling to its limiting value provided by the ordinary oscillator damped equation whereas the frequency of oscillation of remaining six cases declines with the increase in derivative order (damping order).