Applications of the extended fractional Euler-Lagrange equations model to freely oscillating dynamical systems

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2016

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Publishing House of the Romanian Academy

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Department of Mechatronics Engineering
Our purpose in the program is to educate our students for contributing to universal knowledge by doing research on contemporary mechatronics engineering problems and provide them with design, production and publication skills. To reach this goal our post graduate students are offered courses in various areas of mechatronics engineering, encouraged to do research to develop their expertise and their creative side, as well as develop analysis and design skills.
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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

The fractional calculus and the calculus of variations are utilized to model and control complex dynamical systems. Those systems are presented more accurately by means of fractional models. In this study, an extended version of the fractional Euler-Lagrange equations is introduced. In these equations the damping force term is extended to be proportional to the fractional derivative of the displacement with variable fractional order. The finite difference methods and the Coimbra fractional derivative are used to approximate the solution of the introduced fractional Euler-Lagrange equations model. The free oscillating single pendulum system is investigated. © 2016, Editura Academiei Romane. All rights reserved.

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Keywords

Coimbra fractional derivative, Finite difference methods, Fractional Euler-Lagrange equations, Single pendulum

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Citation

55

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Q3

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Q3

Source

Romanian Journal of Physics

Volume

61

Issue

3-4

Start Page

350

End Page

359

URI

https://hdl.handle.net/20.500.14411/9462

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Scopus