Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 180Citation - Scopus: 192On Fractional Calculus with General Analytic Kernels(Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, DumitruMany possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras(MDPI, 2019) Hashem, Hind; El-Sayed, Ahmed; Baleanu, DumitruThis paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied.Article Citation - WoS: 42Citation - Scopus: 50Mobile Language Learning: Contribution of Multimedia Messages Via Mobile Phones in Consolidating Vocabulary(Springer Heidelberg, 2012) Saran, Murat; Saran, Murat; Seferoglu, Golge; Cagiltay, Kursat; Bilgisayar MühendisliğiThis study aimed at investigating the effectiveness of using multimedia messages via mobile phones in helping language learners in consolidating vocabulary. The study followed a pre-test/post-test quasi-experimental research design. The participants of this study were a group of students attending the English Preparatory School of an English-medium university in Turkey. Six different groups were formed in order to investigate the comparative effectiveness of supplementary vocabulary materials delivered through three different means: via mobile phones, on web pages, and in print form. The multimedia messages in this study included the definitions of words, exemplary sentences, related visual representations, information on word formation, and pronunciations of words. Analyses of the quantitative data showed that using mobile phones had positive effects on students' vocabulary acquisition. The results suggest that mobile phones offer great potential for providing learners with supplementary opportunities to recontextualize, recycle, and consolidate vocabulary.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: 9Citation - Scopus: 8Scattering and Spectral Problems of the Direct Sum Sturm-Liouville Operators(Ministry Communications & High Technologies Republic Azerbaijan, 2017) Allahverdiev, Bilender P.; Uğurlu, Ekin; Ugurlu, Ekin; MatematikIn this paper a space of boundary values is constructed for direct sum minimal symmetric Sturm-Liouville operators and description of all maximal dissipative, maximal accumulative, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions. We construct a selfadjoint dilation of dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.Article Citation - WoS: 3Citation - Scopus: 6Hydrogen Hosting of Nano Scale Boron Clusters(Editura Acad Romane, 2008) Özdoğan, Cem; Bäoyäukata, M.; ÄozdoGan, C.; Gäuvenc, Z.B.; Ortak Dersler BölümüIn this paper the Density Functional Results of hydrogen bonded boron micro clusters with B3LYP/6-311++G(d,p) level of computations will be presented. Energetics and structural stability with their possible stable geome- tries of various selected micro complexes of BmHn (for m and n<11) boron hydrides have been analysed, and their binding energies with HOMO-LUMO energy gaps have been determined. Mainly, e®ects of the number of hydrogen atoms on the structures of the boranes are assessed. Moreover, for the cage con̄gurations their distortions have been investigated for the neutral, anionic and cationic cases. It has been observed that there have been two opposing factors for the cage con̄gurations. One of which is the \peeling' of the cage structures by the hydrogen atoms, and the other one is reforming a smaller cage form simultaneously with the remaining boron atoms inside. This is observed mostly for the odd values of m. From our studies it has been also observed that with the bare boron clusters alone, it is di±cult to increase the capacity of the hydrogen storage. Therefore, further studies are necessary with the boron complexes.Article Citation - WoS: 19Citation - Scopus: 18Best Proximity Point Theorems for Kt-Types Cyclic Orbital Contraction Mappings(House Book Science-casa Cartii Stiinta, 2012) Karapınar, Erdal; Karapinar, Erdal; Petrusel, Gabriela; Taş, Kenan; Tas, Kenan; MatematikIn this manuscript, three new KT-types cyclic orbital contractions are defined and some related best proximity point theorems are given. Also, the notion of KT-type cyclic orbital Meir-Keeler contraction is defined and some fixed point theorems for this class of mappings are proved. The results of this manuscript generalize some theorems, on the same subject, of several authors, such as Kirk-Srinavasan-Veeramani, Eldered-Veeramani and Karpagam-Agrawal.Article Citation - WoS: 2Citation - Scopus: 7A Necessary and Sufficient Condition for Oscillation of Second Order Sublinear Delay Dynamic Equations(Amer inst Mathematical Sciences-aims, 2011) Mert, RazIye; Mert, Raziye; Zafer, Agacik; MatematikTime scale calculus approach allows one to treat the continuous, discrete, as well as more general systems simultaneously. In this article we use this tool to establish a necessary and sufficient condition for the oscillation of a class of second order sublinear delay dynamic equations on time scales. Some well known results in the literature are improved and extended.Article Citation - Scopus: 5A Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations With Distributed Delay(2007) Alzabut, J.O.; Alzabut, Jehad; MatematikA necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.Article Citation - WoS: 5Citation - Scopus: 7Spectral Method Based on Bernstein Polynomials for Coupled System of Fredholm Integral Equations(Ministry Communications & High Technologies Republic Azerbaijan, 2016) Alipour, Mohsen; Baleanu, Dumitru; Baleanu, Dumitru; Karimi, Kobra; MatematikIn this paper, we apply Bernstein basis to solve the coupled system of Fredholm integral equations (CSFIE). This method transforms the problem to a system of linear algebraic equations that easily solvable. On the other hand, convergence analysis of this method is discussed. the examples show that the proposed method is implemented very simple and the results have high accuracy.