Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 4Citation - Scopus: 4Fractional Vector Calculus in the Frame of a Generalized Caputo Fractional Derivative(Univ Politehnica Bucharest, Sci Bull, 2018) Jarad, Fahd; Gambo, Yusuf Ya'u; Baleanu, Dumitru; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikThe authors in [1] recently introduced a new generalized fractional derivative on AC(y)(n)[a ,b] and C-y(n)[a, b], and defined their Caputo version. This derivative contains two parameters and reduces to the classical Caputo derivatives if one of these parameters tend to certain values. From here and after, by generalized Caputo fractional derivative, we refer to the Caputo version of the generalized fractional derivative. This paper studies the generalized Caputo fractional derivative and establishes the Fundamental Theorem of Fractional Calculus (FTFC) in the sense of this derivative. The fundamental results are used in establishing some vital theorems and then applied to vector calculus.Article Citation - WoS: 16Citation - Scopus: 16Comparative Application of Wavelet Approaches To Absorption and Ratio Spectra for the Simultaneous Determination of Diminazene Aceturate and Phenazone in Veterinary Granules for Injection(Govi-verlag Pharmazeutischer verlag Gmbh, 2005) Dinç, E; Baleanu, Dumitru; Kanbur, M; Baleanu, D; MatematikA comparison of two wavelet approaches, Daubechies and reverse Biorthogonal, is described for the quantitative resolution of a binary mixture of diminazene aceturate (DIMA) and phenazone (PHE) in veterinary granules for injection without any chemical separation. These two approaches were specified as db4 (a = 180) and rbior3.7 (a = 125) respectively, after testing the signal analysis parameters for the overlapping absorption spectra and ratio spectra. In the first step db4 (a = 180) was applied to the original absorbance data vector of DIMA and PHE. In the second step rbio3.7 (a = 125) was applied to the ratio spectra data vectors of DIMA using the divisor PHE. The same approach was also subjected to the ratio spectra of PHE using the divisor DIMA. The db4 (a = 180) and rbior3.7 (a = 125) calibration graphs were constructed using the transformation values obtained in the wavelet domain. In the method validation, the wavelet calibration functions were tested using synthetic mixtures and the standard addition technique. The simultaneous quantitative analysis of DIMA and PHE in the commercial veterinary preparation was achieved by the elaborated methods. The assay results were compared with each other and good agreement was observed.Article Citation - WoS: 7Citation - Scopus: 8Psychometric Properties of the Turkish Version of Cohen- Mansfield Agitation Inventory in Patients With Dementia(Gunes Kitabevi Ltd Sti, 2012) Baştuğ, Gülbahar; Ozel-Kizil, E. Tugba; Bastug, Gulbahar; Erdogan, Seyda; Sakarya, Direnc; Durmaz, Nazli; PsikolojiIntroduction: Cohen-Mansfield Agitation Inventory (CMAI) is frequently used in patients with dementia for the assessment of agitation severity. This instrument is especially used in research investigating the severity of behavioral symptoms and their treatment responses. In this study, psychometric properties of the Turkish version of CMAI were investigated in patients with dementia (n=52). Materials and Method: CMAI-Turkish version was applied by face-to-face interview to the caregivers of dementia patients who were admitted to a geriatric psychiatry outpatient clinic. For validity, the correlations between CMAI total scores and Neuropsychiatry Inventory (NPI) total and subscale scores were evaluated. For internal consistency, Cronbach alpha value of the items was calculated. Results: CMAI scores were significantly correlated with NPI scores and Cronbach alpha value of the scale was high (0.89). Conclusion: Turkish version of CMAI is a valid and reliable tool for the assessment of the frequency and severity of agitation behavior. Further studies might evaluate inter-rater reliability of the scale in inpatients with dementia.Article Citation - WoS: 3Citation - Scopus: 5Exact Analytical Solutions for Nonlinear Systems of Conformable Partial Differential Equations Via an Analytical Approach(Univ Politehnica Bucharest, Sci Bull, 2022) Thabet, Hayman; Baleanu, Dumitru; Kendre, Subhash; Baleanu, Dumitru; Peters, James; MatematikMany numerical and analytical methods have been developed for solving Partial Differential Equations (PDEs) and conformable PDEs, most of which provide approximate solutions. Exact solutions, however, are vitally important in the proper understanding of the qualitative features of the concerned phenomena and processes. This paper introduces an effective analytical approach for solving nonlinear systems of conformable space-time PDEs. Moreover, the convergence theorem and error analysis of the proposed method are also shown. An essential benefit of this paper is that it yields exact analytical solutions for some nonlinear dynamical systems of conformable space-time PDEs. The Graphical representations of solutions are shown to confirm the accuracy and efficiency of the suggested method.Article Citation - WoS: 4Citation - Scopus: 5One-Dimension Continuous Wavelet Resolution for the Simultaneous Analysis of Binary Mixture of Benazepril and Hydrochlorothiazide in Tablets Using Spectrophotometric Absorbance Data(Editura Academiei Romane, 2004) Dinç, E; Baleanu, Dumitru; Baleanu, D; MatematikOne-dimensional continuous wavelets transform (CWT) followed by a zero-crossing technique were applied to the quantitative resolution of a binary mixture of benazepril (BE) and hydrochlorothiazide (HCT) in two commercial tablet formulations. UV-spectra in the range of 210.1-300.0 nm, were recorded and transferred as vectors having 900 components into MATLAB 6.5. The analyzed signals corresponding to the above vectors were subjected to three CWT families, namely, Mexican (MEX), Haar (HA) and Daubechies3 (DAUB3) wavelets. For these three families a detailed analysis procedure was performed and we retained only those parameters creating many zero-crossing points for transformed signals. At locations where the wavelet transform of one component vanishes, the value of the mixture's transformed signal is due only to the other component. This allows rapid approximate determination of the concentrations. The above three wavelet bases provided reliable results of the analysis of the mixtures containing BE and HCT in two pharmaceutical tablet formulations.Article Citation - WoS: 11Citation - Scopus: 11Best Proximity Results on Condensing Operators Via Measure of Noncompactness With Application To Integral Equations(Chiang Mai Univ, Fac Science, 2020) Gabeleh, Moosa; Karapınar, Erdal; Asadi, Mehdi; Karapinar, Erdal; MatematikWe prove the best proximity point results for condensing operators on C-class of functions, by using a concept of measure of noncompactness. The results are applied to show the existence of a solution for certain integral equations. We express also an illsutrative examples to indicate the validity of the observed results.Article Citation - WoS: 1Citation - Scopus: 2Motion of a Spherical Particle in a Rotating Parabola Using Fractional Lagrangian(Univ Politehnica Bucharest, Sci Bull, 2017) Baleanu, D.; Baleanu, Dumitru; Asad, J. H.; Alipour, M.; Blaszczyk, T.; MatematikIn this work, the fractional Lagrangian of a particle moving in a rotating parabola is used to obtain the fractional Euler- Lagrange equations of motion where derivatives within it are given in Caputo fractional derivative. The obtained fractional Euler- Lagrange equations are solved numerically by applying the Bernstein operational matrices with Tau method. The results obtained are very good and when the order of derivative closes to 1, they are in good agreement with those obtained in Ref. [10] using Multi step- Differential Transformation Method (Ms-DTM).Article Citation - WoS: 32Citation - Scopus: 33Lie Symmetry Analysis and Exact Solutions of the Time Fractional Gas Dynamics Equation(Natl inst Optoelectronics, 2016) Hashemi, M. S.; Baleanu, Dumitru; Baleanu, D.; MatematikFinding the symmetries of a given fractional differential equation is a hot topic in the field of fractional differentiation and its applications. In this manuscript, the Lie symmetries of the time fractional gas dynamics (TFGD) equation are analyzed and new exact solutions are obtained.Article Citation - WoS: 1Citation - Scopus: 1Solving Existence Problems Via F-Contraction in Modified B-Metric Spaces(Turkic World Mathematical Soc, 2022) Karapinar, E.; Karapınar, Erdal; Sedghi, S.; Shobe, N.; MatematikIn this paper, we introduce a new abstract structure, expanded b-metric, as an natural extension of b-metric. We also define basic topological notions in expanded b -metric to able to investigate the existence of fixed point for such mappings under various F-contractive conditions. We provide example to illustrate the results presented herein.Article Citation - WoS: 5Citation - Scopus: 9Combined Application of Continuous Wavelet Transform-Zero Crossing Technique in the Simultaneous Spectrophotometric Determination of Perindopril and Indapamid in Tablets(Soc Brasileira Quimica, 2009) Pektas, Goezde; Baleanu, Dumitru; Dinc, Erdal; Baleanu, Dumitru; Pektag, Gözde; MatematikSignal processing methods based on the combined use of the continuous wavelet transform (CWT) and zero-crossing technique were applied to the simultaneous spectrophotometric determination of perindopril (PER) and indapamide (IND) in tablets. These signal processing methods do not require any priory separation step. Initially, various wavelet families were tested to identify the optimum signal processing giving the best recovery results. From this procedure, the Haar and Biorthogonal 1.5 continuous wavelet transform (HAAR-CWT and BIOR 1.5-CWT, respectively) were found suitable for the analysis of the related compounds. After transformation of the absorbance vectors by using HAAR-CWT and BIOR 1.5-CWT, the CWT-coefficients were drawn as a graph versus wavelength and then the HAAR-CWT and BIOR 1.5-CWT spectra were obtained. Calibration graphs for PER and IND were obtained by measuring the CWT amplitudes at 231.1 and 291.0 rim in the HAAR-CWT spectra and at 228.5 and 246.8 nm in BIOR 1.5-CWT spectra. respectively. In order to compare the performance of HAAR-CWT and BIOR 1.5-CWT approaches, derivative spectrophotometric (DS) method and HPLC as comparison methods, were applied to the PER-IND samples. In this DS method, first derivative absorbance values at 221.6 for PER and 282.7 nm for IND were used to obtain the calibration graphs. The validation of the CWT and DS signal processing methods was carried out by using the recovery study and standard addition technique. In the following step, these methods were Successfully applied to the commercial tablets containing PER and IND compounds and good accuracy and precision were reported for the experimental results obtained by all proposed signal processing methods.