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Citation - WoS: 141
Citation - Scopus: 145
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.
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.
Citation - Scopus: 57
A Short Survey on the Recent Fixed Point Results on B-Metric Spaces
(Selcuk University, 2018) KARAPINAR,E.
The aim of this short survey is to collect and combine basic notions and results in the fixed point theory in the context of b-metric spaces. It is also aimed to show that there are still enough rooms for several researchers in this interesting direction and a huge application potential. © 2018 Selcuk University. All Rights Reserved.