Search results

Sort By:

Limit search:

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

100%

Baleanu D., Blaszczyk T., Asad J., Alipour M.

Acta Physica Polonica A

2016

vol. 130

issue 3

688-691

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.

The Motion of a Bead Sliding on a Wire in Fractional Sense

100%

Baleanu D., Jajarmi A., Asad J., Blaszczyk T.

Acta Physica Polonica A

2017

vol. 131

issue 6

1561-1564

In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grünwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.

Refine search results

2 Acta Physica Polonica A

1 2017

1 2016

2 Asad J.

2 Baleanu D.

2 Blaszczyk T.

1 Alipour M.

1 Jajarmi A.

Search results

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

The Motion of a Bead Sliding on a Wire in Fractional Sense