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

Now showing 1 - 17 of 17

Citation - WoS: 31
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; Matematik
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 - WoS: 1
Citation - Scopus: 1
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; Solak, Ali Osman; Eksi, Haslet; Guzel, Remziye; 56389; Matematik
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 - WoS: 4
Citation - Scopus: 6
Analysis of UV spectral bands using multidimensional scaling
(Springer London Ltd, 2015) Tenreiro Machado, J. A.; Dinc, Erdal; Baleanu, Dumitru; 6981; Matematik
This 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.
Citation - WoS: 73
Citation - Scopus: 98
Anomalous diffusion models with general fractional derivatives within the kernels of the extended mittag-leffler type functions
(Editura Acad Romane, 2017) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Matematik
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 - WoS: 33
Citation - Scopus: 39
Challenges in fractional dynamics and control theory
(Sage Publications Ltd, 2016) Baleanu, Dumitru; Caponetto, Riccardo; Tenreiro Machado, J. A.; 56389; Matematik
Citation - WoS: 9
Citation - Scopus: 14
Characterization approach to modified glassy carbon electrode-nanofilm system within multidimensional scaling
(Amer Scientific Publishers, 2011) Tenreiro Machado, J. A.; Baleanu, Dumitru; Dinc, Erdal; Solak, All Osman; Eksi, Haslet; Guzel, Remziye; 6981; 192756; Matematik
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 - WoS: 178
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; Matematik
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 - WoS: 19
Citation - Scopus: 20
Fractional calculus analysis of the cosmic microwave background
(Editura Acad Romane, 2013) Tenreiro Machado, J. A.; Stefanescu, Petruta; Tintareanu, Ovidiu; Baleanu, Dumitru; Matematik
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 - WoS: 4
Citation - Scopus: 4
Fractional Differentiation and Its Applications I
(Pergamon-elsevier Science Ltd, 2013) Baleanu, Dumitru; Tenreiro Machado, J. A.; Chen, Wen; 56389; Matematik
Citation - WoS: 2
Citation - Scopus: 2
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; Matematik
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 - WoS: 11
Citation - Scopus: 79
Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators
(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Tenreiro Machado, J. A.; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-Jun; 56389; Matematik
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 - WoS: 3
Citation - Scopus: 3
Multidimensional Scaling for Orthodontic Root Resorption
(Hindawi Ltd, 2013) Preoteasa, Cristina Teodora; Ionescu, Ecaterina; Preoteasa, Elena; Tenreiro Machado, J. A.; Baleanu, Mihaela Cristina; Baleanu, Dumitru; 56389; Matematik
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 - WoS: 0
Citation - Scopus: 0
Numerical solutions for odes with local fractional derivative
(de Gruyter Open Ltd, 2015) Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.; 56389; Matematik
In 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.
Citation - WoS: 8
Citation - Scopus: 9
On A Generalized Laguerre Operational Matrix of Fractional Integration
(Hindawi Ltd, 2013) Bhrawy, A. H.; Baleanu, D.; Assas, L. M.; Tenreiro Machado, J. A.; 56389; Matematik
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 - WoS: 198
Citation - Scopus: 206
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
(Aip Publishing, 2016) Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo; Matematik
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.
Citation - WoS: 26
Citation - Scopus: 22
On Local Fractional Continuous Wavelet Transform
(Hindawi Ltd, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; Tenreiro Machado, J. A.; 56389; Matematik
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 - WoS: 30
Citation - Scopus: 70
Systems of Navier-Stokes Equations On Cantor Sets
(Hindawi Ltd, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.; 56389; Matematik
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.