Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform
D. Baleanua,b, T. Blaszczykc, J.H. Asad d and M. Alipour e
aDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
bInstitute of Space Sciences, P.O. Box, MG-23, 76900 Magurele-Bucharest, Romania
cInstitute of Mathematics, Częstochowa University of Technology, al. Armii Krajowej 21, 42-201 Częstochowa, Poland
dDepartment of Physics, College of Arts and Sciences, Palestine Technical University, P.O. Box 7, Tulkarm, Palestine
eDepartment 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