Sevinik Adıgüzel, Rezan

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https://hdl.handle.net/20.500.14411/6781
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Rezan Sevinik Adıgüzel
Sevinik Adıgüzel, Rezan
S. A. Rezan
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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
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rezan.adiguzel@atilim.edu.tr
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Mathematics
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0000-0002-9181-8566
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Scholarly Output

13

Articles

11

Citation Count

271

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2

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2019 - 201942020 - 20225
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Now showing 1 - 9 of 9
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    Article
    Citation - WoS: 130
    Citation - Scopus: 133
    Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions
    (Springer-verlag Italia Srl, 2021) Sevinik-Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; 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.
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    Article
    Recurrence Relations of the Hypergeometric-Type Functions on the Quadratic-Type Lattices
    (Erdal Karapinar, 2019) Adıgüzel,R.S.; 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.
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    Article
    Citation - WoS: 2
    ON THE LIMIT OF DISCRETE q-HERMITE I POLYNOMIALS
    (Ankara Univ, Fac Sci, 2019) Alwhishi, Sakina; Adıgüzel, Rezan Sevinik; 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.
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    Article
    Citation - WoS: 1
    Uniqueness of Solution for Second Order Nonlinear q-difference Equations With Multi-Point and Integral Boundary Conditions
    (Yokohama Publ, 2022) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Sevinik Adıgüzel, Rezan; Mathematics; 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.
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    Article
    Citation - WoS: 9
    Citation - Scopus: 10
    A Solution To Nonlinear Volterra Integro-Dynamic Equations Via Fixed Point Theory
    (Univ Nis, Fac Sci Math, 2019) Sevinik-Adiguzel, Rezan; Karapinar, Erdal; Erhan, Inci M.; 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.
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    Article
    Citation - WoS: 142
    Citation - Scopus: 150
    On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions
    (Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Aksoy, Umit; Aksoy, Ümit; Karapinar, Erdal; Karapınar, Erdal; Erhan, Inci M.; Erhan, İnci; Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics; Mathematics; Mathematics; 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.
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    Article
    Applications of Non-Unique Fixed Point Theorem of Ciric To Nonlinear Integral Equations
    (int Center Scientific Research & Studies, 2019) Sevinik-Adiguzel, Rezan; Karapinar, Erdal; Erhan, Inci M.; Mathematics
    In this paper we discuss the application of the non-unique fixed point theorem of Ciric to nonlinear Fredholm integral equations. We establish an existence theorem for the solutions of such integral equations and apply the theorem to particular examples.
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    Article
    Citation - WoS: 188
    Citation - Scopus: 140
    On the Solution of a Boundary Value Problem Associated With a Fractional Differential Equation
    (Wiley, 2020) Sevinik Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Mathematics
    The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2
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    Article
    Citation - WoS: 2
    Citation - Scopus: 1
    Spectrum 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; Calisir, Ayse Dogan; Mathematics
    In 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.