Numerical solution of the fractional Euler-Lagrange’s equations of a thin elastica model

In this manuscript, we investigated the fractional thin elastic system. We studied the obtained fractional Euler-Lagrange’s equations of the system numerically. The numerical study is based on Grünwald–Letnikov approach, which is power series expansion of the generating function. We present an illus...

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Bibliographic Details
Published inNonlinear dynamics Vol. 81; no. 1-2; pp. 97 - 102
Main Authors Baleanu, Dumitru, Asad, Jihad H., Petras, Ivo
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.07.2015
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Elastic systems
Elastica
Engineering
Euler-Lagrange equation
Mathematical models
Mechanical Engineering
Original Paper
Power series
Series expansion
Vibration
Thin elastica
Fractional Euler-Lagrange equations
Vibration
Grünwald–Letnikov approach
Riemann–Liouville derivatives
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Summary:In this manuscript, we investigated the fractional thin elastic system. We studied the obtained fractional Euler-Lagrange’s equations of the system numerically. The numerical study is based on Grünwald–Letnikov approach, which is power series expansion of the generating function. We present an illustrative example of the proposed numerical model of the system.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-015-1975-7