TR Dizin İndeksli Yayınlar Koleksiyonu / TR Dizin Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14365/4
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Article Citation - WoS: 17Citation - Scopus: 19Lebesgue-Stieltjes Measure on Time Scales(Scientific Technical Research Council Turkey-Tubitak, 2009-01-01) Deniz, Ash; Ufuktepe, ÜnalThe theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory oil time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes Delta and del-measures and by using these measures, we define ail integral adapted to time scales, specifically Lebesgue-Stieltjes Delta-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes Delta-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes Delta-integral.Article Citation - WoS: 3Citation - Scopus: 3A Reduced Computational Matrix Approach With Convergence Estimation for Solving Model Differential Equations Involving Specific Nonlinearities of Quartic Type(Scientific Technical Research Council Turkey-Tubitak, 2020-01-20) Kürkçü, ÖmÜr KıvançThis study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-alpha, matrix equations, and Chebyshev-Lobatto collocation points. The simplicity of the method provides fast computation while eliminating an algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes the consistency of the solutions due to the parameter-alpha. The oscillatory behavior of the obtained solutions on long time intervals is simulated via a coupled methodology involving the proposed method and Laplace-Pade technique. The convergence estimation is established via residual function. Numerical and graphical results are indicated to discuss the validity and efficiency of the method.Article Citation - WoS: 11Citation - Scopus: 11A Novel Graph-Operational Matrix Method for Solving Multidelay Fractional Differential Equations With Variable Coefficients and a Numerical Comparative Survey of Fractional Derivative Types(Scientific Technical Research Council Turkey-Tubitak, 2019-01-18) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, MehmetIn this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.Article Citation - WoS: 4Citation - Scopus: 4On the Hilbert Formulas and of Change of Integration Order for Some Singular Integrals in the Unit Circle(Scientific Technical Research Council Turkey-Tubitak, 2018-05-08) Bory Reyes, Juan; Abreu Blaya, Ricardo; Perez De La Rosa, Marco Antonio; Schneider, Baruch; Rosa, Marco Antonio Perez De La; Reyes, Juan Bory; Blaya, Ricardo AbreuWe obtain some analogues of the Hilbert formulas on the unit circle for alpha-hyperholomorphic function theory when alpha is a complex number. Such formulas relate a pair of components of the boundary value of an alpha-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincare-Bertrand formula for the alpha-hyperholomorphic singular integrals in the unit circle is presented.Article Citation - WoS: 11Citation - Scopus: 14Legendre Wavelet Solution of High Order Nonlinear Ordinary Delay Differential Equations(Scientific Technical Research Council Turkey-Tubitak, 2019-05-29) Gumgum, Sevin; Ersoy Ozdek, Demet; Ozaltun, Gokce; Özdek, Demet ErsoyThe purpose of this paper is to illustrate the use of the Legendre wavelet method in the solution of high-order nonlinear ordinary differential equations with variable and proportional delays. The main advantage of using Legendre polynomials lies in the orthonormality property, which enables a decrease in the computational cost and runtime. The method is applied to five differential equations up to sixth order, and the results are compared with the exact solutions and other numerical solutions when available. The accuracy of the method is presented in terms of absolute errors. The numerical results demonstrate that the method is accurate, effectual and simple to apply.Article Citation - WoS: 11Citation - Scopus: 15Legendre Wavelet Solution of Neutral Differential Equations With Proportional Delays(Springer Heidelberg, 2019-04-01) Gumgum, Sevin; Ersoy Özdek, Demet; Özaltun, Gökçe; Bildik, Necdet; Özdek, Demet Ersoy; Kürkçü, Ömür Kıvanç; Sezer, Mehmet; Savaşaneril, Nurcan BaykuşThe aim of this paper is to solve neutral differential equations with proportional delays by using Legendre wavelet method. Using orthonormal polynomials is the main advantage of this method since it enables a decrease in the computational cost and runtime. Some examples are displayed to illustrate the efficiency and accuracy of the proposed method. Numerical results are compared with various numerical methods in literature and show that the present method is very effectual in solving neutral differential equations with proportional delays.