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.Article 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.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: 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.Article Citation - WoS: 30Citation - Scopus: 73Systems of Navier-Stokes Equations on Cantor Sets(Hindawi Ltd, 2013) Baleanu, Dumitru; Tenreiro Machado, J. A.; Yang, Xiao-JunWe present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.Article Citation - WoS: 3Citation - Scopus: 3Multidimensional Scaling for Orthodontic Root Resorption(Hindawi Ltd, 2013) Ionescu, Ecaterina; Preoteasa, Elena; Tenreiro Machado, J. A.; Baleanu, Mihaela Cristina; Baleanu, Dumitru; Preoteasa, Cristina TeodoraThe paper investigates the risk factors for the severity of orthodontic root resorption. The multidimensional scaling (MDS) visualization method is used to investigate the experimental data from patients who received orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, "Carol Davila" University of Medicine and Pharmacy, during a period of 4 years. The clusters emerging in the MDS plots reveal features and properties not easily captured by classical statistical tools. The results support the adoption of MDS for tackling the dentistry information and overcoming noise embedded into the data. The method introduced in this paper is rapid, efficient, and very useful for treating the risk factors for the severity of orthodontic root resorption.Article Citation - WoS: 203Citation - Scopus: 210On Exact Traveling-Wave Solutions for Local Fractional Korteweg-De Vries Equation(Aip Publishing, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo; Yang, Xiao-JunThis paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces. Published by AIP Publishing.Article Citation - WoS: 4Citation - Scopus: 6Analysis of Uv Spectral Bands Using Multidimensional Scaling(Springer London Ltd, 2015) Dinc, Erdal; Baleanu, Dumitru; Tenreiro Machado, J. A.; Machado, J. A. TenreiroThis study describes the change of the ultraviolet spectral bands starting from 0.1 to 5.0 nm slit width in the spectral range of 200-400 nm. The analysis of the spectral bands is carried out by using the multidimensional scaling (MDS) approach to reach the latent spectral background. This approach indicates that 0.1 nm slit width gives higher-order noise together with better spectral details. Thus, 5.0 nm slit width possesses the higher peak amplitude and lower-order noise together with poor spectral details. In the above-mentioned conditions, the main problem is to find the relationship between the spectral band properties and the slit width. For this aim, the MDS tool is to used recognize the hidden information of the ultraviolet spectra of sildenafil citrate by using a Shimadzu UV-VIS 2550, which is in the world the best double monochromator instrument. In this study, the proposed mathematical approach gives the rich findings for the efficient use of the spectrophotometer in the qualitative and quantitative studies.