Percorrer por autor "Baleanu, Dumitru"
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- Absolutely stable difference scheme for a general class of singular perturbation problemsPublication . El-Zahar, Essam R.; Alotaibi, A. M.; Ebaid, Abdelhalim; Baleanu, Dumitru; Machado, J. A. Tenreiro; Hamed, Y. S.This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems.
- Analysis of the nano-surface of a modified glassy carbon electrode by pseudo phase plane methodPublication . Machado, J. A. Tenreiro; Baleanu, Dumitru; Dinç, Erdal; Solak, Ali Osman; Eksi, Haslet; Güzel, RemziyeThis 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-nanofilm 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.
- Analysis of UV spectral bands using multidimensional scalingPublication . Machado, J. A. Tenreiro; Dinç, Erdal; Baleanu, DumitruThis 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.
- Analysis of UV spectral bands using multidimensional scalingPublication . Machado, J. A. Tenreiro; Dinç, Erdal; Baleanu, DumitruThis 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 ShimadzuUV–VIS 2550, which is in theworld 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.
- Application of Continuous Wavelet Transform to the Analysis of the Modulus of the Fractional Fourier Transform Bands for Resolving Two Component MixturePublication . Dinç, Erdal; Machado, J. A. Tenreiro; Duarte, Fernando Baltazar; Baleanu, DumitruIn 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 a 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.
- Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixturePublication . Dinç, Erdal; Duarte, Fernando B.; Machado, J. A. Tenreiro; Baleanu, DumitruIn 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 a 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.
- Challenges in fractional dynamics and control theoryPublication . Baleanu, Dumitru; Caponetto, Riccardo; Machado, J. A. TenreiroFractional integro-differentiation (or, non-integer order integro-differentiation) is a mathematical framework that leads to efficient tools for modeling and control many of physical systems. Nevertheless, the overall area is commonly refereed as Fractional Calculus (FC) and become popular during the last years. In fact, FC can be used to describe in a solid and compact form systems characterized by long-range temporal or spatial dependence phenomena. Furthermore, the extension of classical and modern control theories to the new perspective, allows the development of algorithms applicable both integer and non-integer order systems
- Characterization approach to modified glassy carbon electrode-nanofilm system within multidimensional scalingPublication . Machado, J. A. Tenreiro; Baleanu, Dumitru; Dinç, Erdal; Solak, Ali Osman; Eksi, Haslet; Güzel, RemziyeThe 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.
- Fractional calculus analysis of the cosmic microwave backgroundPublication . Machado, J. A. Tenreiro; Stefanescu, Petruta; Tintareanu, Ovidiu; Baleanu, DumitruCosmic 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.
- Fractional calculus: a survey of useful formulasPublication . Valério, D.; Trujillo, Juan J.; Rivero, Margarita; Machado, J. A. Tenreiro; Baleanu, DumitruThis paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.
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