Baleanu, DumitruUllah, Malik ZakaBaleanu, Dumitru2022-03-012022-03-012020Ullah, Malik Zaka; Baleanu, Dumitru (2020). "A new type of equation of motion and numerical method for a harmonic oscillator with left and right fractional derivatives", Chinese Journal of Physics, Vol. 68, pp. 712-722.2309-9097https://hdl.handle.net/20.500.12416/5060The aim of this research is to propose a new fractional Euler-Lagrange equation for a harmonic oscillator. The theoretical analysis is given in order to derive the equation of motion in a fractional framework. The new equation has a complicated structure involving the left and right fractional derivatives of Caputo-Fabrizio type, so a new numerical method is developed in order to solve the above-mentioned equation effectively. As a result, we can see different asymptotic behaviors according to the flexibility provided by the use of the fractional calculus approach, a fact which may be invisible when we use the classical Lagrangian technique. This capability helps us to better understand the complex dynamics associated with natural phenomena.eninfo:eu-repo/semantics/closedAccessFractional CalculusEuler-Lagrange EquationCaputo-Fabrizio DerivativeHarmonic OscillatorPosition-Dependent MassArticle6871272210.1016/j.cjph.2020.10.012