Browsing by Author "Tenreiro Machado, J. A."

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Citation Count: Yang, Xiao-Jun...et al. (2016). "A new numerical technique for local fractional diffusion equation in fractal heat transfer", Journal of Nonlinear Sciences and Applications, Vol. 9, No. 10, pp. 5621-5628.
A new numerical technique for local fractional diffusion equation in fractal heat transfer
(Int Scientific Research Publications, 2016) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Gao, Feng; 56389
In this paper, a new numerical approach, embedding the differential transform (DT) and Laplace transform (LT), is firstly proposed. It is considered in the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer. (C) 2016 All rights reserved.
Citation Count: Baleanu, D...et al. (2014). "Advanced Topics in Dynamics of Complex Systems", Mathematical Problems in Engineering, Vol. 2014.
Advanced Topics in Dynamics of Complex Systems
(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Ahmad, Bashir; Nieto, Juan J.; Tenreiro Machado, J. A.; 56389
Citation Count: Tenreiro Machado, J. A...et al. (2012). "Analysis of the Nano-Surface of a Modified Glassy Carbon Electrode by Pseudo Phase Plane Method" Journal of Computational and Theoretical Nanoscience, Vol. 8, No. 10, pp. 1986-1992.
Analysis of the Nano-Surface of A Modified Glassy Carbon Electrode By Pseudo Phase Plane Method
(Amer Scientific Publishers, 2011) Tenreiro Machado, J. A.; Baleanu, Dumitru; Dinc, Erdal; Eksi, Haslet; Solak, Ali Osman; 56389
This 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.
Citation Count: Yang, X.J., Tenreiro Machado, J.A., Baleanu, D. (2017). Anomalous diffusion models with general fractional derivatives within the kernels of the extended mittag-leffler type functions. Romanian Reports In Physics, 69(4).
Anomalous diffusion models with general fractional derivatives within the kernels of the extended mittag-leffler type functions
(Editura Academiei Romane, 2017) Yang, Xiao Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru
This 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.
Citation Count: Baleanu, Dumitru; Caponetto, Riccardo; Tenreiro Machado, J. A., "Challenges in fractional dynamics and control theory", Journal of Vibration and Control, Vol. 22, No. 9, pp. 2151-2152, (2016).
Challenges in fractional dynamics and control theory
(Sage Publications LTD, 2016) Baleanu, Dumitru; Caponetto, Riccardo; Tenreiro Machado, J. A.; 56389
Citation Count: Tenreiro Machado, J.A...et al. (2011). Characterization approach to modified glassy carbon electrode-nanofilm system within multidimensional scaling. Journal of Computational and Theoretical Nanoscience, 8(2), 268-273. http://dx.doi.org/10.1166/jctn.2011.1688
Characterization approach to modified glassy carbon electrode-nanofilm system within multidimensional scaling
(Amer Scientific Publishers, 2011) Tenreiro Machado, J. A.; Baleanu, Dumitru; Dinç, Erdal; Solak, Ali Osman; Ekşi, Haslet; Güzel, Remziye; 6981; 192756
The aim of this work is to characterize the nanofilm consisting of the benzoic acid-modified glassy carbon (GC) electrode system through multidimensional scaling space analysis. The surface modification is based on the electrochemical reaction between the GC electrode and benzoic acid-diazonium salt (BA-DAS). As a result, the nonofilms regarding the benzoic acid-glassy carbon (BA-GC) electrode surface was obtained. For the analysis of the naonfilm of BC-GC electrode system, the IR spectra of the modified BA-GC electrode surface, GC surface and BA-DAS were recorded in the spectral range of 599.84 - 3996.34 [cm(-1)]. The IR data vectors of the above three forms were processed by the using the multidimensional scaling space approach to demonstrate the existence of a nanofilm on the modified BA-GC electrode system. Two- and three-dimensional MDS profiles obtained by application of multidimensional scaling approach to the data sets {CG1, ... ,CG10}, {BA-GC1, ... ,BA-GC10} and {FILM1, ... ,FILM10} allow a good recognition of the nanofilm on the modified glassy carbon (GC) electrode system
Citation Count: Exact Traveling-Wave Solution For Local Fractional Boussinesq Equation in Fractal Domain. (2017) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru, Fractals-Complex Geometry Patterns And Scaling in Nature And Society, 25(4)
Exact Traveling-Wave Solution For Local Fractional Boussinesq Equation In Fractal Domain
(World Scientific Publ CO PTE LTD, 2017) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; 56389
The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.
Citation Count: Tenreiro Machado, J.A...et al. (2013). Fractional calculus analysis of the cosmic microwave background. Romanian Reports in Physics, 65(1), 316-323.
Fractional calculus analysis of the cosmic microwave background
(Editura Academiei Romane, 2013) Tenreiro Machado, J. A.; Stefanescu, Petruta; Tintereanu, Ovidiu; Baleanu, Dumitru
Cosmic 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.
Citation Count: Baleanu, Dumitru; Tenreiro Machado, J. A.; Chen, Wen, "Fractional Differentiation and Its Applications I", Computers & Mathematics With Applications, 66, No. 5, pp. 575-575, (2013).
Fractional Differentiation and Its Applications I
(Pergamon-Elsevier Science LTD, 2013) Baleanu, Dumitru; Tenreiro Machado, J. A.; Chen, Wen; 56389
Citation Count: Tenreiro Machado, J. A.; Zaman, Sharif F.; Baleanu, Dumitru, "Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes", Central European Journal of Physics, Vol. 11, No. 6, pp. 881-885, (2013).
Fractional Order Modelling of Zero Length Column Desorption Response For Adsorbents With Variable Particle Sizes
(Sciendo, 2013) Tenreiro Machado, J. A.; Zaman, Sharif F.; Baleanu, Dumitru; 56389
This 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.
Citation Count: Baleanu, Dumitru...et al. (2014). "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators", Abstract and Applied Analysis.
Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators
(Hindawi LTD, 2014) Baleanu, Dumitru; Tenreiro Machado, J. A.; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-Jun; 56389
We 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.
Citation Count: Preoteasa, Cristina Teodora...et al. (2013). "Multidimensional Scaling for Orthodontic Root Resorption",Mathematıcal Problems In Engineering.
Multidimensional Scaling for Orthodontic Root Resorption
(Hindawi LTD, 2013) Preoteasa, Cristina Teodora; Lonescu, Ecaterina; Preoteasa, Elena; Tenreiro Machado, J. A.; Baleanu, Mihaela Cristina; Baleanu, Dumitru; 56389
The 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.
Citation Count: Bhrawy, A. H...et al. (2013). "On a Generalized Laguerre Operational Matrix of Fractional Integration", Mathematical Problems In Engineering.
On A Generalized Laguerre Operational Matrix of Fractional Integration
(Hindawi LTD, 2013) Bhrawy, A. H.; Baleanu, Dumitru; Assas, L. M.; Tenreiro Machado, J. A.; 56389
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.
Citation Count: Yang, X.J...et al. (2016). On exact traveling-wave solutions for local fractional Korteweg-de Vries equation. Chaos, 26(8). http://dx.doi.org/10.1063/1.4960543
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
(Amer Inst Physics, 2016) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo
This 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
On Local Fractional Continuous Wavelet Transform
(Hindawi LTD, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; Tenreiro Machado, J. A.; 56389
We introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A."Systems of Navier-Stokes Equations on Cantor Sets", Mathematical Problems In Engineering, (2013)
Systems of Navier-Stokes Equations On Cantor Sets
(Hindawi Publishing Corporation, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.; 56389
We 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.