Next Article in Journal / Special Issue
The Fractional Orthogonal Derivative
Previous Article in Journal
Maxwell–Lorentz Electrodynamics Revisited via the Lagrangian Formalism and Feynman Proper Time Paradigm
Previous Article in Special Issue
Asymptotic Expansions of Fractional Derivatives andTheir Applications
Article Menu

Export Article

Open AccessArticle
Mathematics 2015, 3(2), 258-272; doi:10.3390/math3020258

Fractional Euler-Lagrange Equations Applied to Oscillatory Systems

University of São Paulo at Pirassununga, Av. Duque de Caxias Norte, 225-13635-900, Pirassununga-SP, Brazil
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 4 March 2015 / Accepted: 15 April 2015 / Published: 20 April 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
View Full-Text   |   Download PDF [1856 KB, uploaded 20 April 2015]   |  

Abstract

In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional nonlinear dynamic equations involving two classical physical applications: “Simple Pendulum” and the “Spring-Mass-Damper System” to both integer order calculus (IOC) and fractional order calculus (FOC) approaches. The numerical simulations were conducted and the time histories and pseudo-phase portraits presented. Both systems, the one that already had a damping behavior (Spring-Mass-Damper) and the system that did not present any sort of damping behavior (Simple Pendulum), showed signs indicating a possible better capacity of attenuation of their respective oscillation amplitudes. This implication could mean that if the selection of the order of the derivative is conveniently made, systems that need greater intensities of damping or vibrating absorbers may benefit from using fractional order in dynamics and possibly in control of the aforementioned systems. Thereafter, we believe that the results described in this paper may offer greater insights into the complex behavior of these systems, and thus instigate more research efforts in this direction. View Full-Text
Keywords: Fractional calculus; oscillatory systems; dynamic systems; modeling; simulation. Fractional calculus; oscillatory systems; dynamic systems; modeling; simulation.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

David, S.A.; Valentim, C.A., Jr. Fractional Euler-Lagrange Equations Applied to Oscillatory Systems. Mathematics 2015, 3, 258-272.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top