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

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