Baleanu, DumitruSajjadi, Samaneh SadatAsad, Jihad H.Jajarmi, Amin02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2020-04-302025-09-182020-04-302025-09-182019Jajarmi, A...et al. (2017). "A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach", Frontiers in Physics, Vol. 7.2296-424Xhttps://doi.org/10.3389/fphy.2019.00196https://hdl.handle.net/123456789/10614Asad, Jihad/0000-0002-6862-1634In 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.eninfo:eu-repo/semantics/openAccessCoupled OscillatorEuler-Lagrange EquationsFractional DerivativeNonsingular KernelNumerical MethodArticle10.3389/fphy.2019.001962-s2.0-85076685778