Numerical Study for Fractional Euler--Lagrange Equations of a Harmonic Oscillator on a Moving Platform.

We investigate the fractional harmonic oscillator on a moving platform. We obtained the fractional Euler-Lagrange equation from the derived fractional Lagrangian of the system which contains left Caputo fractional derivative. We transform the obtained differential equation of motion into a corresponding integral one and then we solve it numerically. Finally, we present many numerical simulations. [ABSTRACT FROM AUTHOR]