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

Frontiers in Physics

Amin Jajarmi¹  Samaneh Sadat Sajjadi²  Jihad H. Asad⁴  Dumitru Baleanu⁵ 

[1] Department of Electrical Engineering, University of Bojnord, Bojnord, Iran;Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey;Department of Physics, College of Applied Sciences, Palestine Technical University, Tulkarm, Palestine;Institute of Space Sciences, Magurele–Bucharest, Romania;

关键词: coupled oscillator;    Euler–Lagrange equations;    fractional derivative;    nonsingular kernel;    numerical method;   

DOI  :  10.3389/fphy.2019.00196

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown