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

D. Baleanu
^{a,b}, T. Blaszczyk^{c}, J.H. Asad^{ d} and M. Alipour^{ e}^{a}Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
^{b}Institute of Space Sciences, P.O. Box, MG-23, 76900 Magurele-Bucharest, Romania
^{c}Institute of Mathematics, Częstochowa University of Technology, al. Armii Krajowej 21, 42-201 Częstochowa, Poland
^{d}Department of Physics, College of Arts and Sciences, Palestine Technical University, P.O. Box 7, Tulkarm, Palestine
^{e}Department of Mathematics, Faculty of Basic Science, Babol University of Technology, P.O. Box 4717-1167, Babol, Iran |

Received: December 29, 2015; In final form: June 17, 2016 |

Full Text PDF |

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. |

DOI: 10.12693/APhysPolA.130.688 PACS numbers: 02.60.Jh, 02.60.Nm, 02.10.Ud, 02.30.Vv |