AUTHOR=Jajarmi Amin , Baleanu Dumitru , Sajjadi Samaneh Sadat , Asad Jihad H. 

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 7 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00196

DOI=10.3389/fphy.2019.00196

ISSN=2296-424X

ABSTRACT=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.