Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 9Citation - Scopus: 8Scattering and Spectral Problems of the Direct Sum Sturm-Liouville Operators(Ministry Communications & High Technologies Republic Azerbaijan, 2017) Allahverdiev, Bilender P.; Uğurlu, Ekin; Ugurlu, Ekin; MatematikIn this paper a space of boundary values is constructed for direct sum minimal symmetric Sturm-Liouville operators and description of all maximal dissipative, maximal accumulative, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions. We construct a selfadjoint dilation of dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.Article Citation - WoS: 146Citation - Scopus: 166On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Karapınar, Erdal; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MatematikThe aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.Article Citation - WoS: 5Citation - Scopus: 7Spectral Method Based on Bernstein Polynomials for Coupled System of Fredholm Integral Equations(Ministry Communications & High Technologies Republic Azerbaijan, 2016) Alipour, Mohsen; Baleanu, Dumitru; Baleanu, Dumitru; Karimi, Kobra; MatematikIn this paper, we apply Bernstein basis to solve the coupled system of Fredholm integral equations (CSFIE). This method transforms the problem to a system of linear algebraic equations that easily solvable. On the other hand, convergence analysis of this method is discussed. the examples show that the proposed method is implemented very simple and the results have high accuracy.Article Citation - WoS: 21Citation - Scopus: 18Recent Advances on Metric Fixed Point Theory: a Review(Ministry Communications & High Technologies Republic Azerbaijan, 2023) Karapinar, E.In this note, we underline that some of the recent metric fixed point results overlap or repeat the previously existing corresponding ones. Further, we observe that some recently published results, which we might perceive as a generalization from the first point of view, are in fact equivalent. For the clarification and clearing of the literature, this review paper claims to play a crucial role.Article Citation - WoS: 23Citation - Scopus: 17An Analytical Study of Fractional Delay Impulsive Implicit Systems With Mittag-Leffler Law(Ministry Communications & High Technologies Republic Azerbaijan, 2023) Abdo, Mohammed S.; Jarad, Fahd; Abdeljawad, Thabet; Shah, KamalThe Atangana-Baleanu-Caputo fractional derivative is a novel operator with a non-singular Mittag-Leffler kernel that we use to solve a class of Cauchy problems for delay impulsive implicit fractional differential equations. We also show the existence and uniqueness of the solution to the proposed problem. Our study makes use of the Gro center dot nwall inequality in the context of the Atangana-Baleanu fractional integral. Additionally, by the use of fixed point theorems due to Banach, Schaefer, and nonlinear functional analysis, necessary and sufficient conditions are developed under which the considered problem has at least one solution. By providing a relevant example, the results are demonstrated.