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Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Subject: search.filters.subject.B-Metric Space

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 146
    Citation - Scopus: 166
    On 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.; Matematik
    The 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.
  • Article
    Citation - WoS: 144
    Citation - Scopus: 156
    Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions
    (Springer-verlag Italia Srl, 2021) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Sevinik-Adiguzel, Rezan
    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: 41
    Citation - Scopus: 45
    On Istrescu Type Contractions in B-Metric Spaces
    (Mdpi, 2020) Karapinar, Erdal; Fulga, Andreea; Petrusel, Adrian
    In this paper, we introduce the notions of <mml:semantics>alpha</mml:semantics>-almost Istrtescu contraction of type E and of type <mml:semantics>E</mml:semantics> in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 15
    On Contractions Via Simulation Functions On Extended B-Metric Spaces
    (Univ Miskolc inst Math, 2020) Karapinar, Erdal; Chifu, Cristian
    In this paper, we introduce the notion of an admissible extended Z-contraction mapping in the setting of extended b-metric spaces. As an application, we consider Ulam stability problems based on our contractions. The presented results cover several existing results in the literature.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 35
    Nonlinear F-Contractions on B-Metric Spaces and Differential Equations in the Frame of Fractional Derivatives With Mittag-Leffler Kernel
    (Pergamon-elsevier Science Ltd, 2019) Jarad, Fahd; Karapinar, Erdal; Alqahtani, Badr; Fulga, Andreea
    In this manuscript, we aim to refine and characterize nonlinear F-contractions in a more general framework of b-metric spaces. We investigate the existence and uniqueness of such contractions in this setting. We discuss the solutions to differential equations in the setting of fractional derivatives involving Mittag-Leffler kernels (Atangana-Baleanu fractional derivative) by using nonlinear F-contractions that indicate the genuineness of the presented result. (C) 2019 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 15
    Multiparametric Contractions and Related Hardy-Roger Type Fixed Point Theorems
    (Mdpi, 2020) Karapinar, Erdal; Fulga, Andreea; Lopez de Hierro, Antonio Francisco Roldan; de Hierro, Antonio Francis Coroldán López
    In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed withb-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results.
  • Article
    Citation - WoS: 61
    Citation - Scopus: 83
    Impulsive Caputo-Fabrizio Fractional Differential Equations in B-Metric Spaces
    (de Gruyter Poland Sp Z O O, 2021) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Lazreg, Jamal Eddine; Karaplnar, Erdal
    We deal with some impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces. We make use of alpha-phi-Geraghty-type contraction. An illustrative example is the subject of the last section.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Fixed Point Results for Frum-Ketkov Type Contractions in B-Metric Spaces
    (Mdpi, 2021) Karapinar, Erdal; Petrusel, Gabriela; Chifu, Cristian
    The purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 21
    Fixed Point Theorems for Multi-Valued Contractions in B-Metric Spaces With Applications To Fractional Differential and Integral Equations
    (Ieee-inst Electrical Electronics Engineers inc, 2019) Sarwar, Muhammad; Jarad, Fahd; Shoaib, Muhammad; Abdeljawad, Thabet
    The aim of this manuscript is to establish common fixed points results for multi-valued mappings via generalized rational type contractions in complete b-metric spaces. Using the derived results, existence of solutions to certain integral equations and fractional differential equations in the frame of Caputo fractional derivative are studied. Examples are provided for the authenticity of the presented work.