Browsing by Author "Sevinik-Adiguzel, Rezan"

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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; 02. School of Arts and Sciences; 01. Atılım University
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.
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; 02. School of Arts and Sciences; 01. Atılım University
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.
Citation - WoS: 134
Citation - Scopus: 140
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; 02. School of Arts and Sciences; 01. Atılım University
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.