Scopus İndeksli Yayınlar Koleksiyonu

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

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Institution Author: search.filters.institutionAuthor.Ugurlu, EkinSubject: search.filters.subject.Weyl Theory

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Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Left-Definite Fractional Hamiltonian Systems: Titchmarsh-Weyl Theory
    (Pergamon-Elsevier Science Ltd, 2025) Ugurlu, Ekin
    Hamiltonian systems are useful when formally symmetric boundary value problems generated by ordinary derivatives are considered. However, if the ordinary derivatives are changed by non-integer-order (fractional) derivatives, it is not easy to investigate the corresponding problems. In this paper, we introduce a systematic approach to dealing with fractional boundary value problems by constructing a fractional Hamiltonian system. In particular, we consider a left-definite system, and we construct nested-circles theory (Weyl theory) for this system of equations. Using the Titchmarsh-Weyl function, we prove that at least r-solutions of the 2r-dimensional system of equations should be Dirichlet-integrable on a given interval.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Fractional Hamiltonian Systems: Nested Ellipsoids
    (Pergamon-elsevier Science Ltd, 2025) Ugurlu, Ekin
    In this paper, we introduce a singular fractional-order Hamiltonian system with several spectral parameters. Using the inertia indices of the corresponding Hermitian forms we provide a lower bound for the number of linearly independent integrable-square solutions. Moreover, we introduce the Titchmarsh-Weyl function together with an intermediate theorem on the number of the integrable-square solutions. At the end of the paper, we show that 2-sequential and 4-sequential scalar fractional-order differential equations can be embedded into such Hamiltonian systems.
  • 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: 4
    Citation - Scopus: 4
    Singular Hamiltonian System With Several Spectral Parameters Ii: Odd-Order Case
    (Academic Press inc Elsevier Science, 2019) Ugurlu, Ekin
    In this paper we deal with a singular Hamiltonian system of odd-order with several spectral parameters and we investigate the behavior of the solution of this system at singular point with the aid of the characteristic function theory. Moreover, some results have been introduced for the Weyl-Titchmarsh function for some special Hamiltonian systems of odd-order with several spectral parameters. (C) 2019 Elsevier Inc. All rights reserved.
  • 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.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Singular Hamiltonian System With Several Spectral Parameters
    (Academic Press inc Elsevier Science, 2018) Ugurlu, Ekin
    In this paper, the Weyl-Titchmarsh theory has been constructed for the singular 2n-dimensional (even order) Hamiltonian system with several spectral parameters. In particular, we consider that the left end point of the interval is regular and the right end point of the interval is singular for the Hamiltonian system with several parameters. Using the nested circles approach, we prove that at least n-linearly independent solutions are squarly integrable with respect to some matrix functions. (C) 2018 Elsevier Inc. All rights reserved.