Browsing by Author "Eid, Rajeh"

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A Freely Damped Oscillating Fractional Dynamic System Modeled By Fractional Euler-Lagrange Equations
(Sage Publications Ltd, 2018) Agila, Adel; Baleanu, Dumitru; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; 56389
The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler-Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters.
Applications of the Extended Fractional Euler-Lagrange Equations Model to Freely Oscillating Dynamical Systems
(Editura Academiei Romane, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Eid, Rajeh; İrfanoğlu, Bülent; 56389
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.
On fractional Schrodinger equation in alpha-dimensional fractional space
(Pergamon-Elsevier Science, 2009) Baleanu, Dumitru; Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.
The Schrodinger equation is solved in a-dimensional fractional space with a Coulomb potential proportional to 1/r(beta-2), 2 <= beta <= 4. The wave functions are studied in terms of spatial dimensionality alpha and beta and the results for beta = 3 are compared with those obtained in the literature