Browsing by Author "Baleanu, Dumitru"

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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; Department of Mechatronics Engineering; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.
Citation - WoS: 16
Citation - Scopus: 21
Fractional Dimensional Harmonic Oscillator
(Editura Acad Romane, 2011) Eid, R.; Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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: 28
Citation - Scopus: 32
Fractional Unit-Root Tests Allowing for a Fractional Frequency Flexible Fourier Form Trend: Predictability of Covid-19
(Springer, 2021) Omay, Tolga; Baleanu, Dumitru; Economics; 05. School of Business; 01. Atılım University
In this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function. We provide the asymptotics of the newly proposed test and investigate its small-sample properties. Moreover, we show the best estimators for both fractional frequency and fractional difference operator for our newly proposed test. Finally, an empirical study demonstrates that not considering the structural break and fractional integration simultaneously in the testing process may lead to misleading results about the stochastic behavior of the Covid-19 pandemic.
Citation - WoS: 15
Citation - Scopus: 21
A freely damped oscillating fractional dynamic system modeled by fractional Euler-Lagrange equations
(Sage Publications Ltd, 2018) Agila, Adel; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; Mathematics; Department of Mechatronics Engineering; 02. School of Arts and Sciences; 01. Atılım University
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.
Citation - WoS: 51
Citation - Scopus: 63
On Fractional schrodinger Equation in Α-Dimensional Fractional Space
(Pergamon-elsevier Science Ltd, 2009) Eid, Rajeh; Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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. (C) 2008 Elsevier Ltd. All rights reserved.