Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1650Citation - Scopus: 1877On Conformable Fractional Calculus(Elsevier Science Bv, 2015) Abdeljawad, ThabetRecently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed. (C) 2014 Elsevier By. All rights reserved.Article Edelstein-Type Fixed Point Theorems in Compact Tvs-Cone Metric Spaces(Hacettepe University, 2014) Abdeljawad, ThabetIn this paper we prove two fixed point theorems in compact cone metricspaces over normal cones. The first theorem generalizes Edelstein theorem [8] and is different from the generalization obtained in [11]. Thesecond theorem generalizes the main result in [10] and the first theorem.However, the two theorems fail in different categories. Moreover, different versions of the two theorems are proved in TVS-cone metric spacesby making use of the nonlinear scalarization function used very recentlyby Wei-Shih Du in [A note on cone metric fixed point theory and itsequivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove theequivalence of the Banach contraction principle in cone metric spacesand usual metric spaces.Article Citation - WoS: 142Citation - Scopus: 170On Delta and Nabla Caputo Fractional Differences and Dual Identities(Hindawi Ltd, 2013) Abdeljawad, ThabetWe investigate two types of dual identities for Caputo fractional differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. Two types of Caputo fractional differences are introduced; one of them (dual one) is defined so that it obeys the investigated dual identities. The relation between Riemann and Caputo fractional differences is investigated, and the delta and nabla discrete Mittag-Leffler functions are confirmed by solving Caputo type linear fractional difference equations. A nabla integration by parts formula is obtained for Caputo fractional differences as well.Article Citation - WoS: 62Citation - Scopus: 82Meir-Keeler Α-Contractive Fixed and Common Fixed Point Theorems(Springer international Publishing Ag, 2013) Abdeljawad, ThabetGeneralized Meir-Keeler alpha-contractive functions and pairs are introduced and their fixed and common fixed point theorems are obtained. Also, the so-called generalized Meir-Keeler alpha-f-contractive maps commuting with f are introduced and their coincidence and common fixed point theorems are investigated. New sufficient conditions different from those in (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012) are used. An application to the coupled fixed point is established as well. An example is given to show that the alpha-Meir-Keeler generalization is real. AMS Subject Classification: 47H10, 54H25.Article Citation - WoS: 85Citation - Scopus: 101Dual Identities in Fractional Difference Calculus Within Riemann(Springeropen, 2013) Abdeljawad, ThabetWe investigate two types of dual identities for Riemann fractional sums and differences. The first type relates nabla- and delta-type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. These dual identities insist that in the definition of right fractional differences, we have to use both nabla and delta operators. The solution representation for a higher-order Riemann fractional difference equation is obtained as well.Article Citation - WoS: 27Citation - Scopus: 26Completion of Cone Metric Spaces(Hacettepe Univ, Fac Sci, 2010) Abdeljawad, ThabetIn this paper a completion theorem for cone metric spaces and a com- pletion theorem for cone normed spaces are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the scalar norm of the Banach space E.