Sevinik Adıgüzel, Rezan

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S., Rezan
Rezan Sevinik Adıgüzel
Sevinik Adıgüzel, Rezan
S. A. Rezan
R.,Sevinik Adıgüzel
Rezan, Sevinik Adiguzel
Rezan, Sevinik Adıgüzel
Sevinik Adiguzel,Rezan
Sevinik Adıgüzel,R.
Sevinik Adigüzel R.
Sevinik Adiguzel, Rezan
Sevinik Adıgüzel R.
Adlgüzel R.
R., Sevinik Adıgüzel
S.,Rezan
Sevinik Adiguzel,R.
S.A.Rezan
R.,Sevinik Adiguzel
R., Sevinik Adiguzel
Adıgüzel, Rezan Sevinik
Sevinik-Adiguzel, Rezan
Adiguzel, Rezan Sevinik
Adıgüzel,R.S.
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Doçent Doktor
Email Address
rezan.adiguzel@atilim.edu.tr
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Scholarly Output

13

Articles

11

Citation Count

271

Supervised Theses

2

Scholarly Output Search Results

Now showing 1 - 10 of 13
  • Master Thesis
    Hermite ve q-hermite I polinomlarının özellikleri ve aralarındaki limit ilişkileri üzerine
    (2017) Sevinik Adıgüzel, Rezan; Adıgüzel, Rezan Sevinik; Turan, Mehmet; Mathematics
    Bu tezde Hermite polinomları ve ayrık q-Hermite I polinomlarının bazı önemli özellikleri sunulmaktadır. Bu polinomların özellikleri aynı tarzda ele alınacaktır. Ayrık q-Hermite I polinomları, Hermite polinomlarının q-analoğudur. Bu tip polinomlar klasik ortogonal polinomlar ve q-analoğunun önemli bir sınıfıdır. Bu tezdeki temel düşünce, Hermite polinomları ve bunların ayrık versiyonlarının sahip oldukları hipergeometrik tipte diferansiyel ve q-fark denklemleri, üç terimli yineleme bağıntısı, Rodrigues formülü, ortogonal ilişkileri, üreteç fonksiyon özellikleri üzerine çalışmaktır. Hermite polinomları, q -> 1 limit durumunda ayrık q-Hermite I polinomlarından elde edilmektedir. Bu tezde sunulan her bir özellik için Hermite polinomları ve ayrık q-Hermite I polinomları arasındaki limit ilişkisi ayrıntılı olarak ele alınacaktır.
  • Article
    Citation Count: 123
    ON THE SOLUTIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS VIA GERAGHTY TYPE HYBRID CONTRACTIONS
    (Ministry Communications & High Technologies Republic Azerbaijan, 2021) Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics
    The aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.
  • Article
    Citation Count: 1
    UNIQUENESS OF SOLUTION FOR SECOND ORDER NONLINEAR q-DIFFERENCE EQUATIONS WITH MULTI-POINT AND INTEGRAL BOUNDARY CONDITIONS
    (Yokohama Publ, 2022) Sevinik Adıgüzel, Rezan; Mathematics
    The existence and uniqueness of the solution for the boundary value problem associated with nonlinear second-order q-difference equation is discussed by Banach contraction mapping theorem on b-metric spaces. The problem is converted to an integral equation and investigated via a fixed point problem for an integral operator. Existence and uniqueness conditions for a fixed point of the integral operator are obtained. Moreover, an example is introduced to support the main results.
  • Article
    Citation Count: 0
    Recurrence relations of the hypergeometric-type functions on the quadratic-type lattices
    (Erdal Karapinar, 2019) Sevinik Adıgüzel, Rezan; Mathematics
    The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We introduce some recurrence relations for such solutions by also considering their applications to polynomials on the quadratic-type lattices. © 2019, Erdal Karapinar. All rights reserved.
  • Master Thesis
    Zaman skalasında interpolasyon
    (2022) Sevinik Adıgüzel, Rezan; Adıgüzel, Rezan Sevinik; Erhan, İnci; Mathematics
    Bu tezde, zaman skalasında interpolasyon konusunu inceledik. Keyfi bir zaman skalası üzerinde, Lagrange, sigma-Lagrange, Hermite, sigma-Hermite, Newton ve sigma-Newton polinomlarını tanımladık. Bölünen ve sigma-bölünen farkları tanımlayarak, verilen bir veri kümesi için, Hermite polinomunu kolay yoldan elde etmek amacıyla bölünen farklar tablosu oluşturduk. Verilen bir veri kümesini, zaman skalasının yapısına bağlı olarak polinom olmayabilen fonksiyonlar olan sigma-polinomları ile temsil etmek (interpole etmek) alışılmadık bir yöntemdir. Bu şekilde, zaman skalasında interpolasyon için farklı bir bakış açısı sunmaktayız. Çeşitli zaman skalalarında birçok örnek inceledik. Bu örnekler Matlab ile elde edilen sayısal hesaplamalar ve ilgili grafikler ile desteklenmiştir.
  • Article
    Citation Count: 0
    Stability analysis of an epidemic model with vaccination and time delay
    (Wiley, 2023) Turan, Mehmet; Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Mathematics
    This paper presents an epidemic model with varying population, incorporating a new vaccination strategy and time delay. It investigates the impact of vaccination with respect to vaccine efficacy and the time required to see the effects, followed by determining how to control the spread of the disease according to the basic reproduction ratio of the disease. Some numerical simulations are provided to illustrate the theoretical results.
  • Article
    Citation Count: 0
    ON THE LIMIT OF DISCRETE q-HERMITE I POLYNOMIALS
    (Ankara Univ, Fac Sci, 2019) Turan, Mehmet; Alwhishi, Sakina; Sevinik Adıgüzel, Rezan; Turan, Mehmet; Mathematics
    The main purpose of this paper is to introduce the limit relationsbetween the discrete q-Hermite I and Hermite polynomials such that the orthogonality property and the three-terms recurrence relations remain valid.The discrete q-Hermite I polynomials are the q-analogues of the Hermite polynomials which form an important class of the classical orthogonal polynomials.The q-di§erence equation of hypergeometric type, Rodrigues formula and generating function are also considered in the limiting case.
  • Article
    Citation Count: 106
    Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions
    (Springer-verlag Italia Srl, 2021) Aksoy, Ümit; Aksoy, Umit; Sevinik Adıgüzel, Rezan; Erhan, İnci; Karapınar, Erdal; Mathematics
    This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.
  • Article
    Citation Count: 9
    A Solution to Nonlinear Volterra Integro-Dynamic Equations via Fixed Point Theory
    (Univ Nis, Fac Sci Math, 2019) Sevinik Adıgüzel, Rezan; Erhan, İnci; Erhan, Inci M.; Karapınar, Erdal; Mathematics
    In this paper we discuss the existence and uniqueness of solutions of a certain type of nonlinear Volterra integro-dynamic equations on time scales. We investigate the problem in the setting of a complete b-metric space and apply a fixed point theorem with a contractive condition involving b-comparison function. We use the theorem to show the existence of a unique solution of some particular integro-dynamic equations.
  • Article
    Citation Count: 0
    Spectrum of a q-deformed Schrödinger equation by means of the variational method
    (Wiley, 2023) Turan, Mehmet; Turan, Mehmet; Sevinik Adıgüzel, Rezan; Mathematics
    In this work, the q-deformed Schr & ouml;dinger equations defined in different form of the q-Hamiltonian for q-harmonic oscillator are considered with symmetric, asymmetric, and non-polynomial potentials. The spectrum of the q-Hamiltonian is obtained by using the Rayleigh-Ritz variational method in which the discrete q-Hermite I polynomials are taken as the basis. As applications, q-harmonic, purely q-quartic, and q-quartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the q-version of Gaussian potential for an example of a non-polynomial symmetric potential and a specific example of q-version of asymmetric double well potential are presented. Numerous results are given for these potentials for several values of q. The limit relation as q ? 1(-) is discussed. The obtained results of ground-and excited-state energies of the purely q-quartic oscillator and the accuracy of the ground-state energy levels are compared with the existing results. Also, the results are compared with the classical case appearing in the literature in the limiting case q?1(-).