TR-Dizin İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/396

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    Citation - WoS: 2
    Citation - Scopus: 3
    An Asymptotic-Numerical Hybrid Method for Singularly Perturbed System of Two-Point Reaction-Diffusion Boundary-Value Problems
    (Tubitak Scientific & Technological Research Council Turkey, 2019) Cengizci, Suleyman; Natesan, Srinivasan; Atay, Mehmet Tank; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik Fakültesi
    This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.
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    Existence of Positive Solutions for Nonlinear Multipoint P-Laplacian Dynamic Equations on Time Scales
    (Tubitak Scientific & Technological Research Council Turkey, 2020) Dogan, Abdulkadir; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik Fakültesi
    In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.
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    Citation - WoS: 1
    Citation - Scopus: 1
    Existence Results for a Class of Boundary Value Problems for Fractional Differential Equations
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Dogan, Abdulkadir; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik Fakültesi
    By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the LeraySchauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).
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    Solutions to Nonlinear Second-Order Three-Point Boundary Value Problems of Dynamic Equations on Time Scales
    (Tubitak Scientific & Technological Research Council Turkey, 2019) Dogan, Abdulkadir; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik Fakültesi
    In this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional p-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; 24: 295-304].