Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 5Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by Fbm With Noncompact Semigroup Via Mönch Fixed Point(Springer Basel Ag, 2024) Kasinathan, Ramkumar; Kasinathan, Ravikumar; Chalishajar, Dimplekumar; Sandrasekaran, Varshini; Baleanu, DumitruThe aim of this work is to study the mild solutions for a class of impulsive neutral stochastic functional integrodifferential equations driven by fractional Brownian motion using noncompact semigroup in a Hilbert space. We assume that the linear part has a resolvent operator not necessarily compact but the operator norm is continuous. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Monch fixed point theorem. Furthermore, under some suitable assumptions, the considered system's trajectory (T-) controllability is established using generalized Gronwall's inequality. An example is delivered to illustrate the obtained theoretical results. Finally, real life fermentation example is discussed to supporting the proposed system.Article Citation - WoS: 2Citation - Scopus: 1Stability Analysis, Existence and Uniqueness of Solutions for a Fractional Conformable P-Laplacian Coupled Boundary Value Problem on the Disilane Graph(Springer Basel Ag, 2024) Wang, Guotao; Yuan, Hualei; Baleanu, DumitruDisilane is an important inorganic compound, which is widely used in many fields. This study first focuses on investigating the existence and uniqueness of solutions to fractional conformable coupled boundary value problem with the p-Laplacian operator on the disilane graph. The fixed point theorem is used to analyze these results. Additionally, the study also discusses the Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the given problem. At the end of this paper, some examples are presented to illustrate the obtained theorems.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: 46Citation - Scopus: 47Existence of Mild Solutions To Hilfer Fractional Evolution Equations in Banach Space(Springer Basel Ag, 2020) Abdeljawad, Thabet; Sousa, J. Vanterler da C.; Jarad, FahdIn this paper, we investigate the existence of mild solutions to semilinear evolution fractional differential equations with non-instantaneous impulses, using the concepts of equicontinuous (alpha,beta)-resolvent operator function P-alpha,P-beta(t) and Kuratowski measure of non-compactness in Banach space Omega.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.