Browsing by Author "Adiguzel, Rezan Sevinik"

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Citation - WoS: 143
Citation - Scopus: 155
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; 02. School of Arts and Sciences; 01. Atılım University
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.
Spectrum of a Q-Deformed Schrödinger Equation by Means of the Variational Method
(Wiley, 2023) Calisir, Ayse Dogan; Turan, Mehmet; Adiguzel, Rezan Sevinik; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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(-).
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; 02. School of Arts and Sciences; 01. Atılım University
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.
Citation - WoS: 3
Citation - Scopus: 3
Stability Analysis of an Epidemic Model With Vaccination and Time Delay
(Wiley, 2023) Turan, Mehmet; Adiguzel, Rezan Sevinik; Koc, F.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.
Citation - WoS: 2
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; 02. School of Arts and Sciences; 01. Atılım University
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.