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Citation - WoS: 17
Citation - Scopus: 22
Fractional Dimensional Harmonic Oscillator
(Editura Acad Romane, 2011) Eid, R.; Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Mathematics
The fractional Schrodinger equation corresponding to the fractional oscillator was investigated. The regular singular points and the exact solutions of the corresponding radial Schrodinger equation were reported.
Citation - WoS: 48
APPLICATIONS OF THE EXTENDED FRACTIONAL EULER-LAGRANGE EQUATIONS MODEL TO FREELY OSCILLATING DYNAMICAL SYSTEMS
(Editura Acad Romane, 2016) Agila, Adel; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent
The fractional calculus and the calculus of variations are utilized to model and control complex dynamical systems. Those systems are presented more accurately by means of fractional models. In this study, an extended version of the fractional Euler-Lagrange equations is introduced. In these equations the damping force term is extended to be proportional to the fractional derivative of the displacement with variable fractional order. The finite difference methods and the Coimbra fractional derivative are used to approximate the solution of the introduced fractional Euler-Lagrange equations model. The free oscillating single pendulum system is investigated.