Matematik Bölümü

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Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1) -dimensional WBBM equation
(20) Jarad, Fahd; Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A.; 234808
The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the M-fractional (3 + 1)-dimensional Wazwaz-Benjamin-Bona-Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using (1/G′), modified (G′/G2) and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitary wave, periodic wave, kink and antikink waves and most important supernonlinear periodic wave. © 2023 World Scientific Publishing Company.
A Nagumo-like uniqueness theorem for fractional differential equations
(IOP Publishing Ltd, 30) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal
We extend to fractional differential equations a recent generalization of the Nagumo uniqueness theorem for ordinary differential equations of first order
Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function
(202) Baleanu, Dumitru; Ajaj, Ahmed M.; Al-Saidi, Nadia M. G.; Baleanu, Dumitru; 56389
The science of strategy (game theory) is known as the optimal decision-making of autonomous and challenging players in a strategic background. There are different strategies to complete the optimal decision. One of these strategies is the similarity technique. Similarity technique is a generalization of the symmetric strategy, which depends only on the other approaches employed, which can be formulated by altering diversities. One of these methods is the fractal theory. In this investigation, we present a new method studying the similarity analytic solution (SAS) of a 3D-fractal nanofluid system (FNFS). The dynamic evolution is completely given by the concept of differential subordination and majorization. Subordination and majorization relationships are the sets of observable individualities. Game theory can simplify the conditions under which particular sets combine. We offer an explicit construction for the complex possible velocity, energy and thermal functions of two-dimensional fluid flow (the complex variable is suggested in the open unit disk, where the disk is selected at a constant temperature and concentration with uniform velocity). We establish that whenever the 3D-fractal nanofluid system is approximated by a fractal function, the solution has the same property, so a class of fractal tangent function gives SAS. Finally, we demonstrate some simulations and examples that give the consequences of this methodology.
The confined system approximation for solving non-separable potentials in three dimensions
(1998) Taşeli, H.; Eid, R.
The Hubert space L2(ℝ3), to which the wavefunction of the three-dimensional Schrödinger equation belongs, has been replaced by L2(Ω), where Ω is a bounded region. The energy spectrum of the usual unbounded system is then determined by showing that the Dirichlet and Neumann problems in L2(Ω) generate upper and lower bounds, respectively, to the eigenvalues required. Highly accurate numerical results for the quartic and sextic oscillators are presented for a wide range of the coupling constants.
Hamilton-Jacobi quantization of the finite-dimensional systems with constraints
(Editrice Copmpositori Bologna, 1999) Baleanu, Dumitru; Güler, Yurdahan; 56389
The Hamiltonian treatment of constrained systems in Guler's formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a Jacobi system. The main aim of this paper is to investigate the quantization of the finite-dimensional systems with constraints using the canonical formalism introduced by Guler. This approach is applied for two systems with constraints and the results are in agreement with those obtained by Dirac's canonical quatization method and path integral quantization method.
Quantization of Floreanini-Jackiw chiral harmonic oscillator
(Editrice Copmpositori Bologna, 1999) Baleanu, Dumitru; Güler, Yurdahan; 56389
The Floreanini-Jackiw formulation for the chiral quantum mechanical system oscillator is a model of constrained theory with only second-class constraints in Dirac's classification. The covariant quantization needs an infinite number of auxiliary variables and a Wess-Zumino term. In this paper we investigate the path integral quatization of this model using Guler's canonical formalism. All variables are gauge variables in Guler's formalism. Siegel's action is obtained using Hamilton-Jacobi formulation of the systems with constraints.
Higher order finite element solution of the one-dimensional Schrodinger equation
(Wiley, 1999) Eid, R.
The one-dimensional Schrodinger equation has been examined by means of the confined system defined on a finite interval. The eigenvalues of the resulting bounded problem subject to the Dirichlet boundary conditions are calculated accurately to 20 significant figures using higher order shape functions in the usual isoparametric finite element method. Numerical results are given for an arbitrary polynomial potential of degree M. (C) 1999 John Wiley & Sons, Inc.
Lax tensors and separable coordinates in (2+1) dimensions
(2000) Baleanu, Dumitru; Baskal, S.; 56389
We study the Lax tensors of the separable coordinates in (2+1) dimensions. The Lax tensors of the dual manifolds are investigated.
A general treatment of singular Lagrangians with linear velocities
(Editrice Copmpositori Bologna, 2000) Baleanu, Dumitru; Güler, Y.; 56389
The Hamilton-Jacobi treatment of singular systems with linear velocities is investigated. Since the rank of Hessian matrix is zero, all the generalized coordinates are independent parameters. Integrability conditions reduce the degrees of freedom. Path integral quantization is analyzed.
Geometrization of the Lax pair tensors
(World Scientific Publ CO PTE LTD, 2000) Baleanu, Dumitru; Baskal, S.; 56389
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.
On the construction of the phase space of a singular system
(Editrice Copmpositori Bologna, 2000) Baleanu, Dumitru; Güler, Yılmaz; 56389
In this work we present a method for obtaining the true degrees of freedom for the singular systems using the canonical transformations in the Hamilton-Jacobi formalism. The validity of our proposal has been tested by two examples of singular Lagrangians and the results are in agreement with those obtained by other methods.
Hamilton-Jacobi treatment of fields with constraints
(2000) Baleanu, Dumitru; Güler, Y.; 56389
In this paper Güler's formalism for the systems with finite degrees of freedom is applied to the field theories with constraints. The integrability conditions are investigated and the path integral quantization is performed using the action given by Hamilton-Jacobi formulation. Proca's model is investigated in details.
Symmetries of NUT-Kerr-Newman dual metrics
(Editrice Copmpositori Bologna, 2001) Baleanu, Dumitru; 56389
The symmetries of NUT-Kerr-Newman (NUT-KN) dual metrics are analysed. The NUT-Kerr-Newman dual spinning space is constructed in the presence of torsion.
Hamilton-Jacobi quantization of constrained systems
(Inst Physics Acad Sci Czech Republic, 2001) Baleanu, Dumitru; Güler, Yılmaz; 56389
The path integral quantization of contrained systems is analysed using Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac's method.
Spectrophotometric multicomponent analysis of a mixture of metamizol, acetaminophen and caffeine in pharmaceutical formulations by two chemometric techniques
(Pergamon-Elsevier Science LTD, 2001) Baleanu, Dumitru; Baleanu, Dumitru; Onur, Feyyaz; 56389
Inverse least squares (ILS) and factor-based (principal component analysis (PCA)) techniques were proposed for the spectrophotometric multicomponent analysis of a ternary mixture consisting of metamizol, acetaminophen and caffeine, without prior separation. In these chemometric techniques, the measurements of the absorbance values were realized in the spectral range from 225 to 285 nm in the intervals of Delta lambda = 5 nm at the 13 wavelengths in the zero-order spectra of the different ternary mixtures of these active ingredients in 0.1 M HCl. The prepared calibrations of both techniques using the absorbance data and concentration matrix data sets were used to predict the concentration of the unknown concentrations of metamizol acetaminophen and caffeine in their ternary mixture. The 'MAPLE V' software was used for the numerical calculations, Mean recoveries and relative standard deviations for ILS and PCA techniques were found to be 99.8 and 1.68%, 99.9 and 1,66% for caffeine, 99.8 and 1.84%, 100.4 and 2.85% for metamizol, and 99.7 and 1.04%, 99.6 and 1.34/ for acetaminophen, respectively, for the first and second techniques. The techniques were successfully applied to two pharmaceutical formulations marketed in Turkey and results were compared with a new high-performance liquid chromatography method. (C) 2001 Elsevier Science B.V. All rights reserved.
Hamilton-Jacobi treatment of chiral schwinger model
(Kluwer Academic, 2001) Baleanu, Dumitru; Güler, Yılmaz; 56389
We investigate the path integral quantization of the bosonic chiral Schwinger model using multi-Hamilton-Jacobi procedure. The integrability conditions require the extension of the initial phase space. The Wess-Zumino term was recovered calculating the action corresponding to the extended system.
The hamilton-jacobi treatment of supersymmetric quantum mechanics
(World Scientific Publ CO PTE LTD, 2001) Baleanu, Dumitru; Güler, Yurdahan; 56389
We 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.
Hamilton-Jacobi treatment of a non-relativistic particle on a curved space
(IOP Publishing LTD, 2001) Baleanu, Dumitru; Güler, Yurdahan; 56389
In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.
Multi-Hamilton-Jacobi quantization of O(3) nonlinear sigma model
(World Scientific Publ CO PTE LTD, 2001) Baleanu, Dumitru; Güler, Yurdahan; 56389
The 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.
Dual metrics for a class of radiative space-times
(World Scientific Publ CO PTE LTD, 2001) Baleanu, Dumitru; Baskal, S.; 56389
Second-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.

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