Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 73Citation - Scopus: 98Anomalous Diffusion Models With General Fractional Derivatives Within the Kernels of the Extended Mittag-Leffler Type Functions(Editura Acad Romane, 2017) Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.; Baleanu, Dumitru; Machado, J. A. Tenreiro; MatematikThis paper addresses the new general fractional derivatives (GFDs) involving the kernels of the extended Mittag-Leffler type functions (MLFs). With the aid of the GFDs in the MLF kernels, the mathematical models for the anomalous diffusion of fractional order are analyzed and discussed. The proposed formulations are also used to describe complex phenomena that occur in heat transfer.Article Citation - WoS: 19Citation - Scopus: 20Fractional Calculus Analysis of the Cosmic Microwave Background(Editura Acad Romane, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Stefanescu, Petruta; Tintareanu, Ovidiu; Baleanu, Dumitru; MatematikCosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.Book Part Numerical Solutions for Odes With Local Fractional Derivative(de Gruyter Open Ltd, 2015) Baleanu, Dumitru; Tenreiro Machado, J. A.; Yang, Xiao-Jun; Machado, J. A. TenreiroIn this chapter an efficient numerical algorithm for solving ODEs using the extended differential transform method via the generalized local fractional Taylor theorem is presented. Four examples are studied in order to illustrate the proposed technique.Editorial Citation - WoS: 4Citation - Scopus: 4Fractional Differentiation and Its Applications I(Pergamon-elsevier Science Ltd, 2013) Tenreiro Machado, J. A.; Chen, Wen; Baleanu, DumitruArticle Citation - WoS: 2Citation - Scopus: 2Fractional Order Modelling of Zero Length Column Desorption Response for Adsorbents With Variable Particle Sizes(Sciendo, 2013) Zaman, Sharif F.; Baleanu, Dumitru; Tenreiro Machado, J. A.; Machado, J.A.TenreiroThis manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.Article Citation - WoS: 11Citation - Scopus: 79Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets Within Local Fractional Operators(Hindawi Publishing Corporation, 2014) Tenreiro Machado, J. A.; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-Jun; Baleanu, DumitruWe perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.Article Citation - WoS: 26Citation - Scopus: 22On Local Fractional Continuous Wavelet Transform(Hindawi Ltd, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-JunWe introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.Editorial Citation - WoS: 33Citation - Scopus: 39Challenges in Fractional Dynamics and Control Theory(Sage Publications Ltd, 2016) Caponetto, Riccardo; Tenreiro Machado, J. A.; Baleanu, Dumitru; Machado, J.A. TenreiroArticle Citation - WoS: 1Citation - Scopus: 1Analysis of the Nano-Surface of a Modified Glassy Carbon Electrode by Pseudo Phase Plane Method(Amer Scientific Publishers, 2011) Baleanu, Dumitru; Dinc, Erdal; Solak, Ali Osman; Eksi, Haslet; Guzel, Remziye; Tenreiro Machado, J. A.; MacHado, J.A. TenreiroThis paper presents the Pseudo phase plane (PPP) method for detecting the existence of a nanofilm on the nitroazobenzene-modified glassy carbon electrode (NAB-GC) system. This modified electrode systems and nitroazobenze-nanofilnn were prepared by the electrochemical reduction of diazonium salt of NAB at the glassy carbon electrodes (GCE) in nonaqueous media. The IR spectra of the bare glassy carbon electrodes (GCE), the NAB-GC electrode system and the organic NAB film were recorded. The IR data of the bare GC, NAB-GC and NAB film were categorized into five series consisting of FILM1, GC-NAB1, GC1; FILM2, GC-NAB2, GC2; FILM3, GC-NAB3, GC3 and FILM4, GC-NAB4, GC4 respectively. The PPP approach was applied to each group of the data of unmodified and modified electrode systems with nanofilm. The results provided by PPP method show the existence of the NAB film on the modified GC electrode.Article Citation - WoS: 9Citation - Scopus: 10On a Generalized Laguerre Operational Matrix of Fractional Integration(Hindawi Ltd, 2013) Baleanu, D.; Assas, L. M.; Tenreiro Machado, J. A.; Bhrawy, A. H.A new operational matrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived. The fractional integration is described in the Riemann-Liouville sense. This operational matrix is applied together with generalized Laguerre tau method for solving general linear multiterm fractional differential equations (FDEs). The method has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposed method is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.