Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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  • Article
    Citation - WoS: 82
    Citation - Scopus: 109
    Complete Synchronization of Commensurate Fractional Order Chaotic Systems Using Sliding Mode Control
    (Pergamon-elsevier Science Ltd, 2013) Baleanu, Dumitru; Razminia, Abolhassan
    In this manuscript, we consider a new fractional order chaotic system which exhibits interesting behavior such as two, three, and four scrolls. Such systems can be found extensively in mechatronics and power electronic systems which exhibit self-sustained oscillations. Synchronization between two such systems is an interesting problem either theoretically or practically. Using a sliding mode control methodology, we synchronize a unidirectional coupling structure for the two chaotic systems. Numerical simulations are used to verify the theoretical analysis. Additionally, we report the robustness of the system in the presence of a noise in simulation. (C) 2013 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 14
    Modelling the Advancement of the Impurities and the Melted Oxygen Concentration Within the Scope of Fractional Calculus
    (Pergamon-elsevier Science Ltd, 2014) Baleanu, Dumitru; Atangana, Abdon
    The model describing the mitigation of contamination through ventilation inside a moving waterway polluted via dispersed bases together with connected reduction of liquefied oxygen was investigated within the scope of fractional derivatives. The steady-state cases were investigated using some Caputo derivatives properties. The steady-state solutions in presence and absence of the dispersion were derived in terms of the Mittag-Leffler function. In the case of non-steady state, we derived the solution of the first equation in terms of the a-stable error function via the Laplace transform method. To solve the second equation, we constructed the fractional Green function via the Laplace, Fourier and Mellin transforms. The fractional Green function was expressed by mean of the H-function. Particularly, we presented the selected numerical results a function of distance and a. (C) 2014 Elsevier Ltd. All rights reserved.
  • Conference Object
    Citation - WoS: 59
    Citation - Scopus: 68
    Spectrophotometric Quantitative Determination of Cilazapril and Hydrochlorothiazide in Tablets by Chemometric Methods
    (Pergamon-elsevier Science Ltd, 2002) Baleanu, D; Dinç, E
    Four chemometric methods were applied to simultaneous determination of cilazapril and hydrochlorothiazide in tablets. Classical least-square (CLS), inverse least-square (ILS), principal component regression (PCR) and partial least-squares (PLS) methods do not need any priori graphical treatment of the overlapping spectra of two drugs in a mixture. For all chemometric calibrations a concentration set of the random mixture consisting of the two drugs in 0.1 M HCl and methanol (1:1) was prepared. The absorbance data in the UV-Vis spectra were measured for the 15 wavelength points (from 222 to 276 nm) in the spectral region 210-290 nm considering the intervals of Deltalambda = 4 nm. The calibration of the investigated methods involves only absorbance and concentration data matrices. The developed calibrations were tested for the synthetic mixtures consisting of two drugs and using the Maple V software the chemometric, calculations were performed. The results of the methods were compared each other as well as with HPLC method and a good agreement was found. (C) 2002 Elsevier Science B.V. All rights reserved.
  • Article
    Citation - WoS: 58
    Citation - Scopus: 68
    Spectrophotometric Multicomponent Analysis of a Mixture of Metamizol, Acetaminophen and Caffeine in Pharmaceutical Formulations by Two Chemometric Techniques
    (Pergamon-elsevier Science Ltd, 2001) Baleanu, D; Onur, F; Dinç, E
    Inverse least squares (ILS) and factor-based (principal component analysis (PCA)) techniques were proposed for the spectrophotometric multicomponent analysis of a ternary mixture consisting of metamizol, acetaminophen and caffeine, without prior separation. In these chemometric techniques, the measurements of the absorbance values were realized in the spectral range from 225 to 285 nm in the intervals of Delta lambda = 5 nm at the 13 wavelengths in the zero-order spectra of the different ternary mixtures of these active ingredients in 0.1 M HCl. The prepared calibrations of both techniques using the absorbance data and concentration matrix data sets were used to predict the concentration of the unknown concentrations of metamizol acetaminophen and caffeine in their ternary mixture. The 'MAPLE V' software was used for the numerical calculations, Mean recoveries and relative standard deviations for ILS and PCA techniques were found to be 99.8 and 1.68%, 99.9 and 1,66% for caffeine, 99.8 and 1.84%, 100.4 and 2.85% for metamizol, and 99.7 and 1.04%, 99.6 and 1.34/ for acetaminophen, respectively, for the first and second techniques. The techniques were successfully applied to two pharmaceutical formulations marketed in Turkey and results were compared with a new high-performance liquid chromatography method. (C) 2001 Elsevier Science B.V. All rights reserved.
  • Article
    Citation - WoS: 90
    Citation - Scopus: 94
    Stability of Q-Fractional Non-Autonomous Systems
    (Pergamon-elsevier Science Ltd, 2013) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, Dumitru
    In this manuscript, using Lyapunov's direct method, the stability of non-autonomous systems within the frame of the q-Caputo fractional derivative is studied. The conditions for stability, uniform stability and asymptotic stability are discussed. (C) 2012 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 87
    Citation - Scopus: 96
    On Electromagnetic Field in Fractional Space
    (Pergamon-elsevier Science Ltd, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
    Laplacian equation in fractional space describes complex phenomena of physics. With this view, potential of charge distribution in fractional space is derived using Gegenbauer polynomials. Multipoles and magnetic field of charges in fractional space have been obtained. (C) 2008 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 39
    Citation - Scopus: 50
    Kkm Mappings in Cone Metric Spaces and Some Fixed Point Theorems
    (Pergamon-elsevier Science Ltd, 2010) Abuloha, Muhib; Abdeljawad, Thabet; Turkoglu, Duran
    In this paper, we define KKM mappings in cone metric spaces and define NR-cone metric spaces to obtain some fixed point theorems and hence generalize the results obtained in [A. Amini, M. Fakhar, J. Zafarani, KKM mapping in metric spaces, Nonlinear Anal. 60 (2005) 1045-1052]. (C) 2009 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 54
    Citation - Scopus: 66
    On Fractional Schrodinger Equation in Α-Dimensional Fractional Space
    (Pergamon-elsevier Science Ltd, 2009) Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Eid, Rajeh
    The Schrodinger equation is solved in a-dimensional fractional space with a Coulomb potential proportional to 1/r(beta-2), 2 <= beta <= 4. The wave functions are studied in terms of spatial dimensionality alpha and beta and the results for beta = 3 are compared with those obtained in the literature. (C) 2008 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 28
    Citation - Scopus: 33
    Existence of Periodic Solutions, Global Attractivity and Oscillation of Impulsive Delay Population Model
    (Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.
    In this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the population. (c) 2006 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 56
    Citation - Scopus: 68
    Fractional Multipoles in Fractional Space
    (Pergamon-elsevier Science Ltd, 2007) Baleanu, Dumitru; Muslih, Sami I.
    Gauss' law in alpha-dimensional fractional space is investigated. The electrostatic potential with beta th-order fractional multipole is obtained in alpha-dimensionally fractional space. (c) 2005 Elsevier Ltd. All rights reserved.