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Original Research ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Phys. | doi: 10.3389/fphy.2019.00196

A New Feature of the Fractional Euler-Lagrange Equations for a Coupled Oscillator Using a Nonsingular Operator Approach

 Amin Jajarmi1*,  Dumitru Baleanu2, Samaneh Sadat Sajjadi3 and Jihad H. Asad4
  • 1University of Bojnord, Iran
  • 2Çankaya University, Turkey
  • 3Hakim Sabzevari University, Iran
  • 4Palestine Polytechnic University, Palestine

In this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler-Lagrange equations of motion are constructed. After this point, we extend the classical Lagrangian in fractional sense, and thus, the fractional Euler-Lagrange equations of motion are derived. In this new formulation, we consider a recently introduced fractional operator with Mittag-Leffler nonsingular kernel. We also present an efficient numerical method for solving the latter equations in a proper manner. Due to this new powerful technique, we are able to obtain remarkable physical thinks; indeed, we indicate that the complex behavior of many physical systems is realistically demonstrated via the fractional calculus modelling. Finally, we report our numerical findings to verify the theoretical analysis.

Keywords: Coupled oscillator, Euler-Lagrange equations, Fractional derivative, Nonsingular kernel, Numerical method

Received: 26 Mar 2019; Accepted: 06 Nov 2019.

Copyright: © 2019 Jajarmi, Baleanu, Sajjadi and Asad. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Amin Jajarmi, University of Bojnord, Bojnord, Iran, a.jajarmi@gmail.com