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Title: The motion of a bead sliding on a wire in fractional sense
Baleanu, D
Jajarmi, A
Asad, J. H
Blaszczyk, T
Keywords: Riemann-Liouville derivatives
rotating parabola
Lagrange equation
frational euler equations
Issue Date: Jun-2017
Publisher: Polska Akademia Nauk
Abstract: 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
Appears in Collections:Applied science faculty

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