Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 10 of 10
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    On Some Fractional Operators Generated From Abel's Formula
    (Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, Ekin
    This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup property for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Left-Definite Hamiltonian Systems and Corresponding Nested Circles
    (Tubitak Scientific & Technological Research Council Turkey, 2023) Ugurlu, Ekin
    This work aims to construct the Titchmarsh-Weyl M(A)-theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter A. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Discrete Left-Definite Hamiltonian Systems
    (Wilmington Scientific Publisher, Llc, 2023) Ugurlu, Ekin
    In this paper we consider an even-dimensional discrete Hamiltonian system on the set of nonnegative integers in the left-definite form. Using the inertia indices of the hermitian form related with the solutions of the equation we construct some maximal subspaces of the solution space. After constructing some ellipsoids preserving nesting properties we introduce a lower bound for the number of Dirichlet-summable solutions of the equation. Moreover we introduce a limit-point criterion.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    A New Insight To the Hamiltonian Systems With a Finite Number of Spectral Parameters
    (Taylor & Francis Ltd, 2023) Ugurlu, Ekin
    In this article, we introduce a new first-order differential equation containing a finite number of spectral parameters and some results on the solutions of this equation. In particular, with the aid of the nested-circles approach we share a lower bound for the number of linearly independent square-integrable solutions of the equation. We share some limit-point criterias. Moreover, we show that some known and unknown scalar and matrix differential equations can be embedded into this new first-order equation. Using the obtained results we present some additional results for some system of scalar multiparameter differential equations. Finally, we share some relations between the characteristic function of a regular boundary-value problem and the kernel of related integral operator.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    On the Eigenvalues of Second-Order Boundary-Value Problems
    (Wilmington Scientific Publisher, Llc, 2020) Ugurlu, Ekin
    In this paper we investigate the properties of eigenvalues of some boundary-value problems generated by second-order Sturm-Liouville equation with distributional potentials and suitable boundary conditions. Moreover, we share a necessary condition for the problem to have an infinitely many eigenvalues. Finally, we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of the data.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Singular Dissipative Third-Order Operator and Its Characteristic Function
    (Springer Basel Ag, 2020) Ugurlu, Ekin
    In 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: 2
    Citation - Scopus: 3
    Investigation of the Eigenvalues and Root Functions of the Boundary Value Problem Together With a Transmission Matrix
    (Taylor & Francis Ltd, 2020) Ugurlu, Ekin
    In this paper, we consider a singular even-order Hamiltonian system on the union of two intervals together with appropriate boundary and transmission conditions. For investigating the spectral properties of the problem we pass to the inverse operator with an explicit form and we prove some completeness theorems.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Coordinate-Free Approach for the Characteristic Function of a Fourth-Order Dissipative Operator
    (Taylor & Francis inc, 2019) Ugurlu, Ekin
    In this article, we investigate some spectral properties of a singular dissipative fourth-order dissipative operator in case at the singular point. For this purpose we construct the characteristic function of both maximal simple dissipative operator and completely non-unitary contraction which is the Cayley transform of the dissipative operator. Using the properties of the characteristic operator-function we obtain the related results of the boundary value problem. Moreover we obtain the selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing eigenfunctions by using coordinate-free approach.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 17
    Third-Order Boundary Value Transmission Problems
    (Tubitak Scientific & Technological Research Council Turkey, 2019) Ugurlu, Ekin
    In this paper, we consider some third-order operators with transmission conditions. In particular, it is shown that such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operators associated with the differential operators. After showing that the eigenvalues of the problems are real and discrete we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Singular Multiparameter Dynamic Equations With Distributional Potentials on Time Scales
    (Natl inquiry Services Centre Pty Ltd, 2017) Ugurlu, Ekin
    In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-infinite time scales. At first we construct Weyls theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at least one solution of this equation must be squarely integrable with respect to some multiple function which is of one sign and nonzero on the given time scale. Then using the obtained results for the single dynamic equation with several parameters, we investigate the number of the products of the squarely integrable solutions of the singular several equations with distributional potentials and several parameters.