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Article On the Existence and Uniqueness of Solutions of Fractional Dynamic Equations On Time Scales(Yokohama Publ, 2022) Erhan, Inci M.The existence and uniqueness of solutions of Cauchy problem for a nonlinear Caputo fractional dynamic equation of arbitrary order alpha > 0 is studied. The problem is treated as a fixed point problem posed on a b-metric space. A numerical example is presented to support the theoretical results.Article Citation - WoS: 28Citation - Scopus: 50Non-Unique Fixed Point Results in Extended b-metric Space(Mdpi, 2018) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, we investigate the existence of fixed points that are not necessarily unique in the setting of extended b-metric space. We state some examples to illustrate our results.Article Citation - WoS: 10Citation - Scopus: 12A Note on Meir-Keeler Contractions on Dislocated Quasi-b-metric(Univ Nis, Fac Sci Math, 2017) Karapinar, ErdalIn this manuscript, we show that Meir-Keeler type contractions posses a fixed point in the setting of dislocated quasi-b-metricArticle Citation - WoS: 9Citation - Scopus: 14Sehgal Type Contractions on b-Metric Space(Mdpi, 2018) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, we analyze two discontinuous self-mappings that satisfy Sehgal-type inequalities in the setup of complete b-metric space. The main results of the paper cover and extend a few existing results in the corresponding literature. Furthermore, we give some illustrative examples to verify the effectiveness and strength of our derived results. Thereafter, as an application, we consider the obtained result to aggregate the existence and uniqueness of the solution for nonlinear Fredholm integral equations.Article Citation - WoS: 196Citation - Scopus: 168On 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.The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2Article Citation - WoS: 34Citation - Scopus: 48A Note on Cone b-metric and Its Related Results: Generalizations or Equivalence?(Springer international Publishing Ag, 2013) Du, Wei-Shih; Karapinar, ErdalVery recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given results generalize the existing ones or are equivalent to them.
