Sevinik Adıgüzel, Rezan
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Name Variants
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.
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.
Job Title
Doçent Doktor
Email Address
rezan.adiguzel@atilim.edu.tr
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Scholarly Output
10
Articles
8
Citation Count
271
Supervised Theses
2
10 results
Scholarly Output Search Results
Now showing 1 - 10 of 10
Article Citation Count: 0Spectrum of a q-deformed Schrödinger equation by means of the variational method(Wiley, 2023) Turan, Mehmet; Turan, Mehmet; Sevinik Adıgüzel, Rezan; MathematicsIn 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(-).Article Citation Count: 154On the solution of a boundary value problem associated with a fractional differential equation(Wiley, 2020) Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapinar, Erdal; Erhan, İnci; Karapınar, Erdal; MathematicsThe problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2Article Citation Count: 2Spectrum of the q-Schrodinger equation by means of the variational method based on the discrete q-Hermite I polynomials(World Scientific Publ Co Pte Ltd, 2021) Turan, Mehmet; Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; MathematicsIn this work, the q-Schrodinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of q, and the limiting case as q -> 1 is considered. The Rayleigh-Ritz variational method is adopted to the system. The discrete q-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: q-harmonic, purely q-quartic and q-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.Article Citation Count: 9A 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; MathematicsIn 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.Master Thesis Hermite ve q-hermite I polinomlarının özellikleri ve aralarındaki limit ilişkileri üzerine(2017) Sevinik Adıgüzel, Rezan; Adıgüzel, Rezan Sevinik; Turan, Mehmet; MathematicsBu 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.Master Thesis Zaman skalasında interpolasyon(2022) Sevinik Adıgüzel, Rezan; Adıgüzel, Rezan Sevinik; Erhan, İnci; MathematicsBu 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: 0ON THE LIMIT OF DISCRETE q-HERMITE I POLYNOMIALS(Ankara Univ, Fac Sci, 2019) Turan, Mehmet; Alwhishi, Sakina; Sevinik Adıgüzel, Rezan; Turan, Mehmet; MathematicsThe 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: 106Uniqueness 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; MathematicsThis 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: 0Stability analysis of an epidemic model with vaccination and time delay(Wiley, 2023) Turan, Mehmet; Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; MathematicsThis 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: 0Recurrence relations of the hypergeometric-type functions on the quadratic-type lattices(Erdal Karapinar, 2019) Sevinik Adıgüzel, Rezan; MathematicsThe 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.
