Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 146Citation - Scopus: 166On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Karapınar, Erdal; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MatematikThe 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.Conference Object Citation - WoS: 13Citation - Scopus: 12On Admissible Hybrid Geraghty Contractions(North Univ Baia Mare, 2020) Karapinar, Erdal; Karapınar, Erdal; Petrusel, Adrian; Petrusel, Gabriela; MatematikIn this manuscript, we introduce the notion of admissible hybrid Geraghty contraction and we investigate the existence of fixed points of such mappings in the setting of complete metric spaces. Our results not only extend and generalize several results in the fixed point theory literature, but also unify most of them. We give some corollaries to illustrate the novelty of the main result.Article Citation - WoS: 2Citation - Scopus: 2On Periodic Solutions for Implicit Nonlinear Caputo Tempered Fractional Differential Problems(de Gruyter Poland Sp Z O O, 2024) Bouriah, Soufyane; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, ErdalThe main goal of this article is to study the existence and uniqueness of periodic solutions for the implicit problem with nonlinear fractional differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, two illustrative examples will be demonstrated.Article Citation - WoS: 2Citation - Scopus: 3Abstract Random Differential Equations With State-Dependent Delay Using Measures of Noncompactness(Vilnius Univ, inst Mathematics & informatics, 2024) Heris, Amel; Bouteffal, Zohra; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, ErdalThis paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Frechet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented.Article Citation - WoS: 4Citation - Scopus: 4Fixed Point Theorems for Basic Θ-Contraction and Applications(North Univ Baia Mare, 2024) Cvetkovic, Marija; Karapinar, Erdal; Petrusul, Drian; Petruşel, AdrianThe main aim of this paper is omitting some superfluous assumptions in the definition of the class of functions Theta, by means of which were defined and studied various classes of theta-contractions, and still obtaining the uniqueness of the fixed point for this new type of contractive mappings. Several generalizations of continuous theta-contractions are presented along with their applications to the study of integral equations.Article Citation - WoS: 2Citation - Scopus: 4Fixed Points of Proinov Type Multivalued Mappings on Quasimetric Spaces(Wiley, 2022) Karapinar, Erdal; Fulga, Andreea; Yesilkaya, Seher SultanIn this paper, we obtain new results which have not been encountered before in the literature, in multivalued quasimetric spaces, inspired by Proinov type contractions. We use admissible function as proving theorems. We also give an example that supports our theorems.Article Citation - WoS: 6Citation - Scopus: 20Discussions on Proinov-Cb Mapping on B-Metric Space(Wiley, 2023) Fulga, Andreea; Karapinar, ErdalIn the present paper, we introduce the notion of Proinov-C-b-contraction mapping and we discuss it within the most interesting abstract structure, namely, b-metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples.Article Citation - WoS: 5Citation - Scopus: 6An Inevitable Note on Bipolar Metric Spaces(Amer inst Mathematical Sciences-aims, 2024) Cvetkovic, Marija; Karapinar, ErdalBipolar metric spaces and related fixed point theorems therein were introduced based on the motivation of measuring the distance between the elements of distinct sets. The question regarding the independence of these results from the analogous results on a fixed point of an induced mapping on a Cartesian product of two sets. We proved that bipolar metric space is metrizable and we presented two different approaches for defining a metric induced by a bipolar metric. Two obtained metric spaces demonstrated the lack of novelty of fixed point theorems for covariant and contravariant contraction.Article Citation - WoS: 24Citation - Scopus: 41Fractional Partial Random Differential Equations With Infinite Delay(Elsevier, 2022) Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, Erdal; Heris, AmelThe present paper deals with some existence results for the Darbou x problem of partial fractional random differential equations with infinite delay. The arguments are based on a random fixed point theorem with stochastic domain combined with the measure of noncompactness.Article Citation - WoS: 4Citation - Scopus: 6Extensions of Meir-Keeler Contraction Via W-Distances With an Application(Univ Kragujevac, Fac Science, 2022) Karapinar, Erdal; Lakzian, Hosein; Chanda, Ankush; Barootkoob, SedighehIn this article, we conceive the notion of a generalized (alpha, psi, q)-Meir-Keeler contractive mapping and then we investigate a fixed point theorem involving such kind of contractions in the setting of a complete metric space via a w-distance. Our obtained result extends and generalizes some of the previously derived fixed point theorems in the literature via w-distances. In addition, to validate the novelty of our findings, we illustrate a couple of constructive numerical examples. Moreover, as an application, we employ the achieved result to earn the existence criteria of the solution of a kind of non-linear Fredholm integral equation.