Uğurlu, Ekin
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Prof. Dr.
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ekinugurlu@cankaya.edu.tr
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Matematik
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Scholarly Output
54
Articles
108
Citation Count
571
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0
54 results
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Now showing 1 - 10 of 54
Article Citation - WoS: 39Citation - Scopus: 38Regular third-order boundary value problems(Elsevier Science inc, 2019) Ugurlu, Ekin; Uğurlu, Ekin; 238990; MatematikIn this paper, we consider some boundary value problems generated by third-order formally symmetric (self-adjoint) regular differential expression and separated, real-coupled and complex-coupled boundary conditions. It is shown that these problems generate self-adjoint operators. Moreover, the dependence of eigenvalues of these problems on the data are studied and some derivatives of the eigenvalues with respect to some elements of data are introduced. (C) 2018 Elsevier Inc. All rights reserved.Article On a new class of fractional operators(2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru; 56389; MatematikThis 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.Article Citation - WoS: 0Citation - Scopus: 1Dependence Of Eigenvalues Of Some Boundary Value Problems(Tsing Hua Univ, dept Mathematics, 2021) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 4971; 238990; MatematikIn 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.Article Citation - WoS: 12Citation - Scopus: 14Singular conformable sequential differential equations with distributional potentials(Natl inquiry Services Centre Pty Ltd, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Jarad, Fahd; Jarad, Fahd; Ugurlu, Ekin; Uğurlu, Ekin; 56389; 234808; 238990; MatematikIn this paper we consider the singular conformable sequential equation with distributional potentials. We present Weyl's theory in the frame of conformable derivatives. Moreover we give two theorems on limit-point case.Article Citation - WoS: 11Citation - Scopus: 10Some singular third-order boundary value problems(Wiley, 2020) Ugurlu, Ekin; Uğurlu, Ekin; 238990; MatematikIn this paper, we consider some singular formally symmetric (self-adjoint) boundary value problems generated by a singular third-order differential expression and separated and coupled boundary conditions. In particular, we consider that the minimal symmetric operator generated by the third-order differential expression has the deficiency indices (3,3). We investigate same spectral properties related with these problems, and we introduce a method to find the resolvent operator.Article Citation - WoS: 4Citation - Scopus: 7Regular fractional dissipative boundary value problems(Springer, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Ugurlu, Ekin; Uğurlu, Ekin; 56389; 238990; MatematikIn this manuscript we present a regular dissipative fractional operator associated with a fractional boundary value problem. In particular, we present two main dissipative boundary value problems and one of them contains the spectral parameter in the boundary conditions. To construct the associated dissipative operator we present a direct sum Hilbert space.Article Citation - WoS: 1Citation - Scopus: 1Direct approach for the characteristic function of a dissipative operator with distributional potentials(Springer Basel Ag, 2020) Ugurlu, Ekin; Uğurlu, Ekin; 238990; MatematikThe main aim of this paper is to investigate the spectral properties of a singular dissipative differential operator with the help of its Cayley transform. It is shown that the Cayley transform of the dissipative differential operator is a completely non-unitary contraction with finite defect indices belonging to the class C-0. Using its characteristic function and the spectral properties of the resolvent operator, the complete spectral analysis of the dissipative differential operator is obtained. Embedding the Cayley transform to its natural unitary colligation, a Caratheodory function is obtained. Moreover, the truncated CMV matrix is established which is unitary equivalent to the Cayley transform of the dissipative differential operator. Furthermore, it is proved that the imaginary part of the inverse operator of the dissipative differential operator is a rank-one operator and the model operator of the associated dissipative integral operator is constructed as a semi-infinite triangular matrix. Using the characteristic function of the dissipative integral operator with rank-one imaginary component, associated Weyl functions are established.Article Citation - WoS: 2Citation - Scopus: 2Singular dissipative third-order operator and its characteristic function(Springer Basel Ag, 2020) Ugurlu, Ekin; Uğurlu, Ekin; 238990; MatematikIn 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: 1Citation - Scopus: 1A new Hamiltonian system(Academic Press inc Elsevier Science, 2020) Ugurlu, Ekin; Uğurlu, Ekin; 238990; MatematikThis paper aims to share a new first-order differential equation that contains the continuous analogous of the orthogonal polynomials on the unit-circle. We introduce some basic results on the system and solutions of the system. Using nested-circle approach we introduce the possible number of square-integrable solutions of the system. At the end of the paper we share a limit-point criteria for the two-dimensional system of equations. (C) 2020 Elsevier Inc. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1Fractional Differential Equation With a Complex Potential(Univ Nis, Fac Sci Math, 2020) Uğurlu, Ekin; Ugurlu, Ekin; Taş, Kenan; Tas, Kenan; Baleanu, Dumitru; Baleanu, Dumitru; 238990; 4971; 56389; MatematikIn this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.
