Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 10Citation - Scopus: 10Solitons of the (1+1)- and (2+1)-Dimensional Chiral Nonlinear Schrodinger Equations With the Jacobi Elliptical Function Method(Springer Basel Ag, 2023) Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper; Tala-Tebue, EricOur objective is to find new analytical solutions of the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Soliton solutions of the considered models are obtained such as, cnoidal solutions, the hyperbolic solutions and the trigonometric solutions. The obtained analytical solutions are new in the literature. The stability conditions of these solutions are also given. The obtained stable solutions are presented graphically for some specific parameters. Moreover, the conditions of modulational instability for both models are provided. The proposed method can be useful to obtain the analytical solutions of nonlinear partial differential equations.Article Quasilinear Coupled System in the Frame of Nonsingular Abc-Derivatives With P-Laplacian Operator at Resonance(Springer Basel Ag, 2024) Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari; Bouloudene, MokhtarWe investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana-Baleanu-Caputo (shortly, ABC) derivatives formulations are based on the well-known Mittag-Leffler kernel utilizing Ge's application of Mawhin's continuation theorem. Examples are provided to demonstrate our findings.Article Citation - WoS: 1On Quantum Star Graphs With Eigenparameter Dependent Vertex Conditions(Springer Basel Ag, 2023) Ugurlu, Ekin; Mutlu, GokhanWe investigate the spectral properties of two different boundary value problems on a compact star graph in which the vertex conditions are dependent on the spectral parameter. We treat these boundary value problems as eigenvalue problems in some extended Hilbert spaces by associating them with vector-valued operators. We prove that the corresponding operators are self-adjoint. We construct the characteristic functions of these eigenvalue problems and prove that the corresponding operators have discrete spectrum. Moreover, we present some examples where we construct fundamental solutions and derive the resolvent operators.Article Citation - WoS: 14Citation - Scopus: 16Bennett-Leindler Type Inequalities for Nabla Time Scale Calculus(Springer Basel Ag, 2021) Kayar, Zeynep; Kaymakcalan, Billur; Pelen, Neslihan NesliyeIn this study, we generalize the converse of Hardy and Copson inequalities, which are known as Bennett and Leindler type inequalities, for nabla time scale calculus. This generalization allows us not only to unify all the related results existing in the literature for an arbitrary time scale but also to obtain new results which are analogous to the results of the delta time scale calculus.Article Citation - WoS: 62Citation - Scopus: 76A Survey:f-Contractions With Related Fixed Point Results(Springer Basel Ag, 2020) Fulga, Andreea; Agarwal, Ravi P.; Karapinar, ErdalIn this note, we aim to review the recent results onF-contractions, introduced by Wardowski. After examining the fixed point results for such operators, we collect the sequent results in this direction in a different setting. One of the aims of this survey is to provide a complete collection of several fixed generalizations and extensions ofF-contractions.Article Citation - WoS: 1Citation - Scopus: 2A Fixed Point Theorem for a System of Pachpatte Operator Equations(Springer Basel Ag, 2021) Ozturk, Ali; Rakocevic, Vladimir; Karapinar, ErdalIn this paper, we investigate sufficient conditions for the existence of solutions to the system {Tx=x, alpha(i)(x)=0(E), i = 1,2, ... r, where 0(E) is the zero vector of E, and alpha(i) : E -> E i = 1, 2, ... , r are mappings, T is a mapping satisfying the Pachpatte-contraction.Article Citation - WoS: 1Citation - Scopus: 1Direct Approach for the Characteristic Function of a Dissipative Operator With Distributional Potentials(Springer Basel Ag, 2020) Ugurlu, EkinThe main aim of this paper is to investigate the spectral properties of a singular dissipative differential operator with the help of its Cayley transform. It is shown that the Cayley transform of the dissipative differential operator is a completely non-unitary contraction with finite defect indices belonging to the class C-0. Using its characteristic function and the spectral properties of the resolvent operator, the complete spectral analysis of the dissipative differential operator is obtained. Embedding the Cayley transform to its natural unitary colligation, a Caratheodory function is obtained. Moreover, the truncated CMV matrix is established which is unitary equivalent to the Cayley transform of the dissipative differential operator. Furthermore, it is proved that the imaginary part of the inverse operator of the dissipative differential operator is a rank-one operator and the model operator of the associated dissipative integral operator is constructed as a semi-infinite triangular matrix. Using the characteristic function of the dissipative integral operator with rank-one imaginary component, associated Weyl functions are established.Article Citation - WoS: 2Citation - Scopus: 2Singular Dissipative Third-Order Operator and Its Characteristic Function(Springer Basel Ag, 2020) Ugurlu, EkinIn this work, we describe well-defined dissipative boundary conditions related with a singular third-order differential equation in lim-3 case at singular point. Using the characteristic function of the corresponding dissipative operator we introduce a completeness theorem.Article Citation - WoS: 8Citation - Scopus: 8A New Method for Dissipative Dynamic Operator With Transmission Conditions(Springer Basel Ag, 2018) Ugurlu, Ekin; Tas, KenanIn this paper, we investigate the spectral properties of a boundary value transmission problem generated by a dynamic equation on the union of two time scales. For such an analysis we assign a suitable dynamic operator which is in limit-circle case at infinity. We also show that this operator is a simple maximal dissipative operator. Constructing the inverse operator we obtain some information about the spectrum of the dissipative operator. Moreover, using the Cayley transform of the dissipative operator we pass to the contractive operator which is of the class With the aid of the minimal function we obtain more information on the dissipative operator. Finally, we investigate other properties of the contraction such that multiplicity of the contraction, unitary colligation with basic operator and CMV matrix representation associated with the contraction.