Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 19Citation - Scopus: 22Approximating System of Ordinary Differential-Algebraic Equations Via Derivative of Legendre Polynomials Operational Matrices(World Scientific Publ Co Pte Ltd, 2023) Abdelhakem, M.; Baleanu, D.; Agarwal, P.; Moussa, HanaaLegendre polynomials' first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.Article Citation - WoS: 10Citation - Scopus: 15Extension of Perturbation Theory To Quantum Systems With Conformable Derivative(World Scientific Publ Co Pte Ltd, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, MohamedIn this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order alpha. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required alpha-corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when alpha = 1.Article Citation - WoS: 1Citation - Scopus: 1A New Approach To Dynamic Finite-Size Scaling(World Scientific Publ Co Pte Ltd, 2003) Gündüç, S; Aydin, M; Gündüç, Y; Dilaver, MIn this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x(0) to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x(0) separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.Article Citation - WoS: 18Citation - Scopus: 21Multi-Hamilton Quantization of O(3) Nonlinear Sigma Model(World Scientific Publ Co Pte Ltd, 2001) Baleanu, D; Güler, WThe O(3) nonlinear sigma model is investigated using multi-Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac's method. By choosing an adequate extension of phase space we describe the transformed system by a set of three Hamilton-Jacobi equations and calculate the corresponding action.Article Citation - WoS: 10Citation - Scopus: 9Dual Metrics for a Class of Radiative Space-Times(World Scientific Publ Co Pte Ltd, 2001) Baskal, S; Baleanu, DSecond-rank nondegenerate Killing tensors for some subclasses of space-times admitting parallel null one-planes ace investigated. Lichnerowicz radiation conditions are imposed to provide a physical meaning to space-times whose metrics are described through their associated second-rank Killing tensors. Conditions under which the dual space-times retain the same physical properties are presented.Article Citation - WoS: 22Citation - Scopus: 26Discrete Fractional Diffusion Equation of Chaotic Order(World Scientific Publ Co Pte Ltd, 2016) Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da; Wu, Guo-ChengDiscrete fractional calculus is suggested in diffusion modeling in porous media. A variable-order fractional diffusion equation is proposed on discrete time scales. A function of the variable order is constructed by a chaotic map. The model shows some new random behaviors in comparison with other variable-order cases.Article Citation - WoS: 10Citation - Scopus: 6Geometrization of the Lax Pair Tensors(World Scientific Publ Co Pte Ltd, 2000) Baskal, S; Baleanu, D; Bakal, S.The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion tensor. Three-dimensional space-times admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.Article Citation - WoS: 144Citation - Scopus: 167Generalized Exponential Rational Function Method for Extended Zakharov-Kuzetsov Equation With Conformable Derivative(World Scientific Publ Co Pte Ltd, 2019) Osman, M. S.; Baleanu, Dumitru; Chanbari, Behzad; Ghanbari, BehzadIn this paper, new analytical obliquely propagating wave solutions for the time fractional extended Zakharov-Kuzetsov (FEZK) equation of conformable derivative are investigated. By using the main properties of the conformable derivative, the FEZK equation is transformed into integer-order differential equations, and the reduced equations are solved via the generalized exponential rational function method (GERFM). The shape and features for the resulting solutions are illustrated through three-dimensional (3D) plots and corresponding contour plots for various values of the free parameters.Article Citation - WoS: 22Citation - Scopus: 26A Nonstandard Finite Difference Scheme for Two-Sided Space-Fractional Partial Differential Equations(World Scientific Publ Co Pte Ltd, 2012) Abu Rqayiq, Abdullah; Baleanu, Dumitru; Momani, Shaher; Rqayiq, Abdullah AbuIn this paper, we apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions.Article Citation - WoS: 35Citation - Scopus: 44Generalized Fractional Order Bloch Equation With Extended Delay(World Scientific Publ Co Pte Ltd, 2012) Daftardar-Gejji, Varsha; Baleanu, Dumitru; Magin, Richard; Bhalekar, SachinThe fundamental description of relaxation (T-1 and T-2) in nuclear magnetic resonance (NMR) is provided by the Bloch equation, an integer-order ordinary differential equation that interrelates precession of magnetization with time-and space-dependent relaxation. In this paper, we propose a fractional order Bloch equation that includes an extended model of time delays. The fractional time derivative embeds in the Bloch equation a fading power law form of system memory while the time delay averages the present value of magnetization with an earlier one. The analysis shows different patterns in the stability behavior for T-1 and T-2 relaxation. The T-1 decay is stable for the range of delays tested (1 mu sec to 200 mu sec), while the T-2 relaxation in this extended model exhibits a critical delay (typically 100 mu sec to 200 mu sec) above which the system is unstable. Delays arise in NMR in both the system model and in the signal excitation and detection processes. Therefore, by adding extended time delay to the fractional derivative model for the Bloch equation, we believe that we can develop a more appropriate model for NMR resonance and relaxation.