Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 4Citation - Scopus: 6A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; MatematikWe investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.Article Citation - WoS: 6Citation - Scopus: 6A Caputo Fractional Order Boundary Value Problem With Integral Boundary Conditions(Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikIn this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.Article Citation - WoS: 2Citation - Scopus: 5Some Fixed Point Results in Tvs-Cone Metric Spaces(House Book Science-casa Cartii Stiinta, 2013) Abdeljawad, T.; Abdeljawad, Thabet; Rezapour, Sh; MatematikEvery TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.Article Citation - WoS: 11Citation - Scopus: 11Best Proximity Results on Condensing Operators Via Measure of Noncompactness With Application To Integral Equations(Chiang Mai Univ, Fac Science, 2020) Gabeleh, Moosa; Karapınar, Erdal; Asadi, Mehdi; Karapinar, Erdal; MatematikWe prove the best proximity point results for condensing operators on C-class of functions, by using a concept of measure of noncompactness. The results are applied to show the existence of a solution for certain integral equations. We express also an illsutrative examples to indicate the validity of the observed results.Article Citation - WoS: 7Citation - Scopus: 7Coupled Fixed Point Theorems for Generalized Symmetric Contractions in Partially Ordered Metric Spaces and Applications(Eudoxus Press, Llc, 2014) Jain, M.; Taş, Kenan; Tas, K.; Rhoades, B. E.; Gupta, N.; MatematikIn the setting of partially ordered metric spaces, we introduce the notion of generalized symmetric g-Meir-Keeler type contractions and use the notion to establish the existence and uniqueness of coupled common fixed points. Our notion extends the notion of generalized symmetric Meir-Keeler contractions given by Berinde et. al. [V. Berinde, and M. Pacurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory and Appl., 2012, 2012:115, doi:10.1186/1687-1812-2012-115] to a pair of mappings. We also give some applications of our main results.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 - Scopus: 3A Note on Sobolev Form Fractional Integro-Differential Equation With State-Dependent Delay Via Resolvent Operators(Cambridge Scientific Publishers, 2017) Mallika, D.; Baleanu, Dumitru; Suganya, S.; Baleanu, D.; Arjunan, M.M.; MatematikThis paper explores the new existence and uniqueness of mild solutions for a class of Sobolev form fractional integro-differential equation (in short SFFIDE) with state-dependent delay (in short SDD) and nonlocal conditions (in short NLCs) via resolvent operators in Banach spaces. By making use of Banach contraction principle and Krasnoselskii fixed point theorem (in short FPT) along with resolvent operators and fractional calculus, we develop the sought outcomes. An illustration is furthermore provided to demonstrate the acquired concepts. © CSP - Cambridge, UK; I & S - Florida, USA, 2017.Article Citation - WoS: 6Citation - Scopus: 5Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces(Univ Osijek, dept Mathematics, 2011) Turkoglu, Duran; Abdeljawad, Thabet; Abuloha, Muhib; Abdeljawad, Thabet; MatematikIn this paper, we proved a fixed point theorem and a common fixed point theorem in cone metric spaces for generalized contraction mappings where some of the main results of Ciric in [8, 27] are recovered.Article Citation - WoS: 1Citation - Scopus: 1Solving Existence Problems Via F-Contraction in Modified B-Metric Spaces(Turkic World Mathematical Soc, 2022) Karapinar, E.; Karapınar, Erdal; Sedghi, S.; Shobe, N.; MatematikIn this paper, we introduce a new abstract structure, expanded b-metric, as an natural extension of b-metric. We also define basic topological notions in expanded b -metric to able to investigate the existence of fixed point for such mappings under various F-contractive conditions. We provide example to illustrate the results presented herein.Article Citation - WoS: 3Completion of Tvs-Cone Metric Spaces and Some Fixed Point Theorems(Gazi Univ, 2011) Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikIn this paper a completion theorem for cone metric spaces and a completion theorem for cone normed space over a complete locally convex topological vector space E are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the topology of the locally convex space E. Very recently some fixed point theorems obtained in cone Banach spaces are generalized to locally convex cone Banach spaces. These theorems can not be generalized or proved trivially by using the nonlinear scalarization function used very recently by Wei-Shih Du in " A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis Theory Methods and Applications 72 (5):2259-2261 (2010)".