Communications in Theoretical Physics ›› 2020, Vol. 72 ›› Issue (5): 055002. doi: 10.1088/1572-9494/ab7700

• Mathematical Physics • Previous Articles     Next Articles

The fractional features of a harmonic oscillator with position-dependent mass

Dumitru Baleanu1,2,Amin Jajarmi3,Samaneh Sadat Sajjadi4,Jihad H Asad5,()   

  1. 1Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
    2Institute of Space Sciences, PO Box MG–23, R 76900, Magurele–Bucharest, Romania
    3Department of Electrical Engineering, University of Bojnord, PO Box 94531–1339, Bojnord, Iran
    4Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran
    5Palestine Technical University, College of Arts and Sciences, Department of Physics, PO Box 7 Tulkarm, Palestine
  • Received: 2019-11-07 Revised: 2020-02-11 Accepted: 2020-02-11 Published: 2020-05-01


In this study, a harmonic oscillator with position-dependent mass is investigated. Firstly, as an introduction, we give a full description of the system by constructing its classical Lagrangian; thereupon, we derive the related classical equations of motion such as the classical Euler–Lagrange equations. Secondly, we fractionalize the classical Lagrangian of the system, and then we obtain the corresponding fractional Euler–Lagrange equations (FELEs). As a final step, we give the numerical simulations corresponding to the FELEs within different fractional operators. Numerical results based on the Caputo and the Atangana-Baleanu-Caputo (ABC) fractional derivatives are given to verify the theoretical analysis.

Key words: position-dependent mass, harmonic oscillator, Euler–Lagrange equations, fractional derivative