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

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Citation Count: Yang, Xiao-Jun...et al. (2017). "A new fractional derivative involving the normalized sinc function without singular kernel", Europan Physical Journal Special-Topic, Vol.226, No.16-18, pp.3567-3575.
A new fractional derivative involving the normalized sinc function without singular kernel
(Springer Heidelberg, 2017) Yang, Xiao-Jun; Gao, Feng; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389
In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.
Citation Count: Sayevand, K.; Machado, J. Tenreiro; Baleanu, D. "A new glance on the Leibniz rule for fractional derivatives", Communications In Nonlinear Science and Numerical Simulation, Vol. 62, pp. 244-249, (2018)
A New Glance On the Leibniz Rule for Fractional Derivatives
(Elsevier Science BV, 2018) Sayevand, K.; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389
This paper proposes a new strategy to study some useful properties of growth rates of functions in C-alpha is an element of R spaces in order to analyze the Leibniz rule for fractional derivatives. The differential operators are taken in the Riemann-Liouville sense. Moreover, stability analysis of the proposed strategy is investigated. The results demonstrate that the proposed theoretical analysis is accurate. (C) 2018 Elsevier B.V. All rights reserved.
Citation Count: Baleanu, Dumitru...et al. (2013). "Advanced Topics in Fractional Dynamics", Advances in Mathematical Physics.
Advanced Topics in Fractional Dynamics
(Hindawi LTD, 2013) Baleanu, Dumitru; Srivastava, H. M.; Daftardar-Gejji, Varsha; Li, Changpin; Machado, J. A. Tenreiro; 56389
Citation Count: Machado, J.A.T., Dinç, E., Baleanu, D. (2015). Analysis of UV spectral bands using multidimensional scaling. Signal Image And Video Processing, 9(3), 573-580. http://dx.doi.org/10.1007/s11760-013-0485-7
Analysis of UV spectral bands using multidimensional scaling
(Springer London LTD, 2015) Machado, J. A. Tenreiro; Dinç, Erdal; Baleanu, Dumitru; 6981
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 Count: Dinç, E...et al. (2015). Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture. Signal Image And Video Processing, 9(4), 801-807. http://dx.doi.org/10.1007/s11760-013-0503-9
Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture
(Springer London LTD, 2015) Dinç, Erdal; Duarte, Fernando B.; Machado, J. A. Tenreiro; Baleanu, Dumitru; 6981
In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.
Citation Count: Valerio, D.; Trujillo, JJ.; Rivero, M., "Fractional calculus: A survey of useful formulas" European Physical Journal-Special Topics, Vol.222, No.8, pp.1827-1846, (2013).
Fractional calculus: A survey of useful formulas
(Springer Heidelberg, 2013) Valerio, D.; Trujillo, J. J.; Rivero, M.; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389
Citation Count: Baleanu, Dumitru; Machado, J. A. Tenreiro, "Fractional differentiation and its applications (FDA08) PREFACE", Physica Scripta, Vol.T136, (2009).
Fractional differentiation and its applications (FDA08) PREFACE
(IOP Publishing LTD, 2009) Baleanu, Dumitru; Machado, J. A. Tenreiro; 56389
Citation Count: Machado, JAT.; Baleanu, Dumitru; Chen, W., "New trends in fractional dynamics" Journal Of Vibration And Control, Vol.20, No.7, pp.963, (2014).
New trends in fractional dynamics
(Sage Publications LTD, 2014) Machado, J. A. Tenreiro; Baleanu, Dumitru; Chen, Wen; Sabatier, Jocelyn; 56389
Citation Count: Yang, XJ.; Baleanu, Dumitru; Machado, JAT, "Numerical solutions for odes with local fractional derivative" Fractional Dynamics, pp.258-271, (2015)
Numerical solutions for odes with local fractional derivative
(De Gruyter Open LTD, 2015) Yang, X. J.; Baleanu, Dumitru; Machado, J. A. Tenreiro; 56389
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 Count: Yang, Xiao-Jun; Baleanu, Dumitru; Machado, J. A. Tenreiro (2014). "On analytical methods for differential equations with local fractional derivative operators", Fractional Calculus: Theory, pp. 65-87.
On analytical methods for differential equations with local fractional derivative operators
(2014) Yang, Xiao-Jun; Baleanu, Dumitru; Machado, J. A. Tenreiro; 56389
This chapter reviews new analytical methods for a family of differential equations with local fractional derivatives. We concentrate mainly on Fourier series, and Fourier and Laplace transforms with local fractional operators. The potential applications of the reported results are discussed.
Citation Count: Yang, Xiao-Jun...et al. (2016). "On Local Fractional Operators View of Computational Complexity Diffusion and Relaxation Defined on Cantor Sets", Vol. 20, pp. S755-S767.
On Local Fractional Operators View of Computational Complexity Diffusion and Relaxation Defined on Cantor Sets
(Vinca Inst, 2016) Yang, Xiao-Jun; Zhang, Zhi-Zhen; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389
This paper treats the description of non-differentiable dynamics occurring in complex systems governed by local fractional partial differential equations. The exact solutions of diffusion and relaxation equations with Mittag-Leffler and exponential decay defined on Cantor sets are calculated. Comparative results with other versions of the local fractional derivatives are discussed.
Citation Count: Baleanu, Dumitru; Machado, J. A. T.; Osman, M. S., "On Nonautonomous Complex Wave Solutions Described By The Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients", Optical and Quantum Electronics, 50, No. 2, (2018).
On Nonautonomous Complex Wave Solutions Described By The Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients
(Springer, 2018) Osman, M. S.; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389
This paper investigates the coupled Schrodinger-Boussinesq equation with variable-coefficients using the unified method. New nonautonomous complex wave solutions are obtained and classified into two categories, namely polynomial function and rational function solutions. For the polynomial functions emerge the complex solitary, complex soliton and complex elliptic wave solutions, while for the rational function are observed complex periodic rational and complex hyperbolic rational wave solutions. The physical insight and the dynamical behavior of the solutions describing the wave propagation in laser or plasma physics are discussed and analysed for different choices of the arbitrary functions in the solutions.
Citation Count: Nigmatullin, R.R...et al. (2015). On the analysis of data emerging in non-linear and complex systems comparison of two x-ray prony spectra. Revista De Chimie, 66(12), 1929-1937.
On the analysis of data emerging in non-linear and complex systems comparison of two x-ray prony spectra
(Chiminform Data SA, 2015) Nigmatullin, Raoul R.; Khramov, A. S.; Kiyamov, A. G.; Fatkhullin, B. F.; Machado, J. A. Tenreiro; Baleanu, Dumitru
New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the "best fit" model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A-("cheap') and B-("expensive') that are used after their proper calibration for the measuring of the same substance (corundum a-Al20). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) -X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to "ideal" experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the I M in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal "filling") are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes
Citation Count: Chen, Wen; Baleanu, Dumitru; Machado, J. A. Tenreiro, "Special issue of computers and mathematics with applications on fractional differentiation and its applications Preface", Computers & Mathematics With Applications, Vol.59, No.5, pp. 1585-1585, (2010).
Special Issue of Computers and Mathematics With Applications On Fractional Differentiation and Its Applications Preface
(Pergamon-Elsevier Science LTD, 2010) Chen, Wen; Baleanu, Dumitru; Machado, J. A. Tenreiro; 56389