WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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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.Article Citation - WoS: 33Citation - Scopus: 35Nonlinear 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, AndreeaIn 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: 61Citation - Scopus: 83Impulsive 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, ErdalWe 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: 18Citation - Scopus: 21Fixed 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, ThabetThe 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.