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2017 | 131 | 6 | 1561-1564
Article title

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

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EN
Abstracts
EN
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.
Publisher

Year
Volume
131
Issue
6
Pages
1561-1564
Physical description
Dates
published
2017-06
received
2017-02-26
Contributors
author
  • Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
  • Institute of Space Sciences, P.O. Box MG-23, 76900, Magurele, Bucharest, Romania
author
  • Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran
author
  • Department of Physics, College of Arts and Sciences, Palestine Technical University, P.O. Box 7, Tulkarm, Palestine
author
  • Institute of Mathematics, Czestochowa University of Technology, al. Armii Krajowej 21, 42-201 Częstochowa, Poland
References
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Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv131n626kz
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