Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Now showing 1 - 10 of 12
  • 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: 13
    Citation - Scopus: 15
    Hardy-Copson Type Inequalities for Nabla Time Scale Calculus
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Kaymakcalan, Billur; Kayar, Zeynep
    This paper is devoted to the nabla unification of the discrete and continuous Hardy?Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
  • 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: 1
    Scattering and Characteristic Functions of a Dissipative Operator Generated by a System of Equations
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Bayram, Elgiz; Tas, Kenan
    In this paper, we consider a system of first-order equations with the same eigenvalue parameter together with dissipative boundary conditions. Applying Lax-Phillips scattering theory and Sz.-Nagy-Foias model operator theory we prove a completeness theorem.
  • Article
    On a Fifth-Order Nonselfadjoint Boundary Value Problem
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Tas, Kenan
    In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator. In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative
  • Article
    Citation - WoS: 13
    Citation - Scopus: 16
    Modeling the Impact of Temperature on Fractional Order Dengue Model With Vertical Transmission
    (Ramazan Yaman, 2020) Defterli, Ozlem
    A dengue epidemic model with fractional order derivative is formulated to an-alyze the effect of temperature on the spread of the vector-host transmitted dengue disease. The model is composed of a system of fractional order differ-ential equations formulated within Caputo fractional operator. The stability of the equilibrium points of the considered dengue model is studied. The cor-responding basic reproduction number R alpha 0 is derived and it is proved that if R alpha 0 < 1, the disease-free equilibrium (DFE) is locally asymptotically stable. L1 method is applied to solve the dengue model numerically. Finally, numerical simulations are also presented to illustrate the analytical results showing the influence of the temperature on the dynamics of the vector-host interaction in dengue epidemics.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    Fourth Order Differential Operators With Distributional Potentials
    (Tubitak Scientific & Technological Research Council Turkey, 2020) Bairamov, Elgiz; Ugurlu, Ekin
    In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.
  • Article
    Coset Algebras of the Maxwell-Einstein Supergravities
    (Tubitak Scientific & Technological Research Council Turkey, 2006) Yılmaz, Nejat Tevfik
    The general structure of the scalar cosets of the Maxwell-Einstein supergravities is given. Following an introduction of the non-linear coset formalism of the supergravity theories a comparison of the coset algebras of the Maxwell-Einstein supergravities in various dimensions is discussed.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 11
    On the Solutions of a Fractional Boundary Value Problem
    (Tubitak Scientific & Technological Research Council Turkey, 2018) Ugurlu, Ekin; Baleanu, Dumitru; Tas, Kenan
    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.
  • 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.