Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus

In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We first give a description to the system by constructing its classical Lagrangian. Secondly, the classical Euler-Lagrange equations (i.e., the classical equations of motion) are derived. Thirdly, we fractionalize the classical Lagrangian of the system, and as a result, we obtain the fractional Euler-Lagrange equations. As the final step, we give the numerical simulations of the fractional model, a new model which is based on Caputo fractional derivative.