TY - JOUR
AU - Jajarmi, Amin
AU - Baleanu, Dumitru
AU - Sajjadi, Samaneh Sadat
AU - Asad, Jihad H.
PY - 2019
M3 - 10.3389/fphy.2019.00196
SP - 196
TI - A New Feature of the Fractional Euler–Lagrange Equations for a Coupled Oscillator Using a Nonsingular Operator Approach
JO - Frontiers in Physics
UR - https://www.frontiersin.org/article/10.3389/fphy.2019.00196
VL - 7
SN - 2296-424X
N2 - 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 non-singular 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 modeling. Finally, we report our numerical findings to verify the theoretical analysis.
ER -