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Article Citation - WoS: 141Citation - Scopus: 144Uniqueness 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.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 - WoS: 25Citation - Scopus: 32Fixed Point Theorems in Complete Modular Metric Spaces and an Application To Anti-Periodic Boundary Value Problems(Univ Nis, Fac Sci Math, 2017) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.In this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Caratheodory's type is considered in the framework of modular metric spaces.Article Citation - WoS: 68FIXED POINTS OF GENERALIZED α-ADMISSIBLE CONTRACTIONS ON b-METRIC SPACES WITH AN APPLICATION TO BOUNDARY VALUE PROBLEMS(Yokohama Publ, 2016) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.A general class of alpha-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations.
