WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 2Citation - Scopus: 2Spectrum of the Q-Schrodinger Equation by Means of the Variational Method Based on the Discrete Q-Hermite I Polynomials(World Scientific Publ Co Pte Ltd, 2021) Turan, Mehmet; Adiguzel, Rezan Sevinik; Calisir, Ayse Dogan; Adlgüzel, Rezan Sevinik; Çallşlr, Ayşe DoǧanIn this work, the q-Schrodinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of q, and the limiting case as q -> 1 is considered. The Rayleigh-Ritz variational method is adopted to the system. The discrete q-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: q-harmonic, purely q-quartic and q-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.Article Citation - WoS: 6Citation - Scopus: 8New Wavelet Method for Solving Boundary Value Problems Arising From an Adiabatic Tubular Chemical Reactor Theory(World Scientific Publ Co Pte Ltd, 2020) Baleanu, Dumitru; Ali, Mohamed R.This paper displays an efficient numerical technique of realizing mathematical models for an adiabatic tubular chemical reactor which forms an irreversible exothermic chemical reaction. At a steady-state solution for an adiabatic rounded reactor, the model can be diminished to a conventional nonlinear differential equation which converts into a system of the nonlinear equation that can proceed numerically utilizing Newton's iterative method. An operational matrix of coordination is derived and is utilized to decrease the model for an adiabatic tubular chemical reactor to an arrangement of algebraic equations. Simple execution, basic activities, and precise arrangements are the fundamental highlights of the proposed wavelet technique. The numerical solutions attained by the present technique have been contrasted and compared with other techniques.Article Citation - WoS: 2Citation - Scopus: 2The Hamilton-Jacobi Treatment of Front-Form Schwinger Model(World Scientific Publ Co Pte Ltd, 2002) Gulerz, Yurdahan; Baleanu, Dumitru; Güler, YurdahanThe Hamilton-Jacobi formalism was applied to quantize the front-form Schwinger model. The importance of the surface term is discussed in detail. The BRST-anti-BRST symmetry was analyzed within Hamilton-Jacobi formalism.Article Citation - WoS: 8Citation - Scopus: 8A Novel Fractional Grey Model Applied To the Environmental Assessment in Turkey(World Scientific Publ Co Pte Ltd, 2020) Arshad, Sadia; Defterli, Ozlem; Xie, Xiaoqing; Baleanu, Dumitru; Shaheen, Aliya; Sheng, JinyongThis study presents a novel fractional order grey model FGM (alpha,1) obtained by extending the grey model (GM (1,1)). For this, we generalize the whitenization first-order differential equation to fractional order by using the Caputo fractional derivative of order alpha. A real-world case study, scrutinize the economic growth influence on environmental degradation in Turkey, is performed to evaluate the significance of the projected model FGM (alpha,1) in contrast to the current classical GM. We apply autoregressive distributed lags bounds testing co-integration approach to empirically examine the long-run and short-run relation among economic growth, agriculture, forestry and fishing (AFF), electricity utilization and CO2 emissions. Using the new fractional order model, all the variables are forecasted in the forthcoming years until 2030. Findings disclose that electricity utilization and economic growth (GDP) accelerate emission of CO2 though in the long run agriculture, forestry, and fishing reduce the environmental pollution in Turkey.Article Citation - WoS: 6Citation - Scopus: 4Symmetries of the Dual Metrics(World Scientific Publ Co Pte Ltd, 2002) Baleanu, DIn this paper the symmetries of the dual manifold are investigated. We found the conditions when the manifold and its dual admit the same Killing vectors and Killing-Yano tensors. The dual conformal Killing vectors and dual conformal Killing-Yano tensors were investigated. In the case of an Einstein's metric g(munu) the corresponding equations for its dual were found. The examples of Kerr-Newman geometry and the separable coordinates in 1 + 1 dimensions axe analyzed in details.Article Citation - WoS: 11Citation - Scopus: 9Dual Metrics and Nongeneric Supersymmetries for a Class of Siklos Space-Times(World Scientific Publ Co Pte Ltd, 2002) Baskal, S; Baleanu, DThe presence of Killing-Yano tensors implies the existence of nongeneric supercharges in spinning point particle theories on curved backgrounds. Dual metrics axe defined through their associated nondegenerate Killing tensors of valence two. Siklos space-times, which are the only nontrivial Einstein spares conformal to nonflat pp-waves are investigated with regard to the existence of their corresponding Killing and Killing-Yano, tensors. It is found that a class of Siklos space-times admit dual metrics and nongeneric supercharges.Article Citation - WoS: 14Citation - Scopus: 14The Hamilton-Jacobi Treatment of Supersymmetric Quantum Mechanics(World Scientific Publ Co Pte Ltd, 2001) Baleanu, D; Güler, YWe study the Hamilton-Jacobi quantization of supersymmetric quantum mechanics. The equations of motion of the Grassmann variables are obtained from the integrability conditions. The results are in agreement with those obtained by Dirac's procedure.Article Citation - WoS: 14Citation - Scopus: 18Efficient Numerical Treatments for a Fractional Optimal Control Nonlinear Tuberculosis Model(World Scientific Publ Co Pte Ltd, 2018) AL-Mekhlafi, S. M.; Baleanu, D.; Sweilam, N. H.In this paper, the general nonlinear multi-strain Tuberculosis model is controlled using the merits of Jacobi spectral collocation method. In order to have a variety of accurate results to simulate the reality, a fractional order model of multi-strain Tuberculosis with its control is introduced, where the derivatives are adopted from Caputo's definition. The shifted Jacobi polynomials are used to approximate the optimality system. Subsequently, Newton's iterative method will be used to solve the resultant nonlinear algebraic equations. A comparative study of the values of the objective functional, between both the generalized Euler method and the proposed technique is presented. We can claim that the proposed technique reveals better results when compared to the generalized Euler method.Article Citation - WoS: 7Citation - Scopus: 7A Numerical Framework for the Approximate Solution of Fractional Tumor-Obesity Model(World Scientific Publ Co Pte Ltd, 2019) Defterli, Ozlem; Shumaila; Arshad, Sadia; Baleanu, DumitruIn this paper, we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and Caputo-Fabrizio (CF). Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed. Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models. We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.Article Citation - WoS: 30Citation - Scopus: 32On a New Modified Fractional Analysis of Nagumo Equation(World Scientific Publ Co Pte Ltd, 2019) Deniz, Sinan; Baleanu, Dumitru; Saad, Khaled M.In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo-Fabrizio and Atangana-Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called h-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.