Browsing by Author "Uğurlu, Ekin"

Now showing 1 - 11 of 11

Citation - WoS: 1
Citation - Scopus: 1
Dependence of Eigenvalues of Some Boundary Value Problems
(Tsing Hua Univ, dept Mathematics, 2021) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 4971; 238990; Matematik
In this work we deal with a system of two first-order differential equations containing the same eigenvalue parameter. We consider some suitable separated real and complex coupled boundary conditions, and show that the eigenvalues generated by this system are continuous in an eigenvalue branch. Also we introduce the ordinary and Frechet derivatives of these eigenvalues with respect to some elements of the data.
Citation - WoS: 7
Citation - Scopus: 6
Dirac Systems With Regular and Singular Transmission Effects
(2017) Uğurlu, Ekin; 238990
In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax Phillips scattering function and Sz-Nagy Foia¸s characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.
Citation - WoS: 3
Citation - Scopus: 3
Dissipative Operator and Its Cayley Transform
(2017) Tas, Kenan; Uğurlu, Ekin; 4971; 238990
In this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter dependent boundary conditions. For this purpose we use the characteristic function of the maximal dissipative operator and inverse operator. This investigation is done by the characteristic function of the Cayley transform of the maximal dissipative operator, which is a completely nonunitary contraction belonging to the class C0. Using Solomyak s method we also introduce the self-adjoint dilation of the maximal dissipative operator and incoming/outgoing eigenfunctions of the dilation. Moreover, we investigate other properties of the Cayley transform of the maximal dissipative operator.
On a new class of fractional operators
(2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru; 56389
This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.
Citation - WoS: 12
On Dilation, Scattering and Spectral Theory for Two-Interval Singular Differential Operators
(Soc Matematice Romania, 2015) Allahverdiev, Bilender P.; Uğurlu, Ekin; Ugurlu, Ekin; 238990; Matematik
This paper aims to construct a space of boundary values for minimal symmetric singular impulsive-like Sturm-Liouville (SL) operator in limit-circle case at singular end points a, b and regular inner point c. For this purpose all maximal dissipative, accumulative and self-adjoint extensions of the symmetric operator are described in terms of boundary conditions. We construct a self-adjoint dilation of maximal dissipative operator, a functional model and we determine its characteristic function in terms of the scattering matrix of the dilation. The theorem verifying the completeness of the eigenfunctions and the associated functions of the dissipative SL operator is proved.
On Singular Fifth-Order Boundary Value Problems With Deficiency Indices (5, 5)
(Math Soc Serbia-drustvo Matematicara Srbije, 2022) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 238990; Matematik
This paper is devoted to introduce a way of construction of the well-defined boundary conditions for the solutions of a singular fifth-order equation with deficiency indices (5, 5). Imposing suitable separated and coupled boundary conditions some properties of the eigenvalues of the problems have been investigated.
On the solutions of a fractional boundary value problem
(2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan; 56389; 4971; 238990
This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
On the solutions of a fractional boundary value problem
(Scientific Technical Research Council Turkey-Tubitak, 2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan; 238990; 4971; 56389
This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
On the solutions of a fractional boundary value problem
(SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan; 238990; 56389; 4971
This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
Citation - WoS: 9
Citation - Scopus: 8
Scattering and Spectral Problems of the Direct Sum Sturm-Liouville Operators
(Ministry Communications & High Technologies Republic Azerbaijan, 2017) Allahverdiev, Bilender P.; Uğurlu, Ekin; Ugurlu, Ekin; 238990; Matematik
In 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.
Citation - WoS: 1
Singular Dirac Systems in the Sobolev Space
(2017) Uğurlu, Ekin; 238990
In this paper we construct Weyl s theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, we describe the behavior of the solution belonging to the Sobolev space around the singular point.