Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article -Simultaneous chemometric determination of pyridoxine hydrochloride and isoniazid in tablets bymultivariate regression methods(Wiley-Blackwell, 2010) Dinç, Erdal; Üstündağ, Ögür; Baleanu, DumitruThe sole use of pyridoxine hydrochloride during treatment of tuberculosis gives rise to pyridoxine deficiency. Therefore, a combination of pyridoxine hydrochloride and isoniazid is used in pharmaceutical dosage form in tuberculosis treatment to reduce this side effect. In this study, two chemometric methods, partial least squares (PLS) and principal component regression (PCR), were applied to the simultaneous determination of pyridoxine (PYR) and isoniazid (ISO) in their tablets. A concentration training set comprising binary mixtures of PYR and ISO consisting of 20 different combinations were randomly prepared in 0.1 M HCl. Both multivariate calibration models were constructed using the relationships between the concentration data set (concentration data matrix) and absorbance data matrix in the spectral region 200-330 nm. The accuracy and the precision of the proposed chemometric methods were validated by analyzing synthetic mixtures containing the investigated drugs. The recovery results obtained by applying PCR and PLS calibrations to the artificial mixtures were found between 100.0 and 100.7%. Satisfactory results obtained by applying the PLS and PCR methods to both artificial and commercial samples were obtained. The results obtained in this manuscript strongly encourage us to use them for the quality control and the routine analysis of the marketing tablets containing PYR and ISO drugs. CopyrightArticle Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1) -dimensional WBBM equation(2023) Siddique, Imran; Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A.The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the M-fractional (3 + 1)-dimensional Wazwaz-Benjamin-Bona-Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using (1/G′), modified (G′/G2) and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitaryArticle Article shape effect of nanosize particles on magnetohydrodynamic nanofluid flow and heat transfer over a stretching sheet with entropy generation(2020) Rashid, Umair; Baleanu, Dumitru; Iqbal, Azhar; Abbas, MuhammdMagnetohydrodynamic nanofluid technologies are emerging in several areas including pharmacology, medicine and lubrication (smart tribology). The present study discusses the heat transfer and entropy generation of magnetohydrodynamic (MHD) Ag-water nanofluid flow over a stretching sheet with the effect of nanoparticles shape. Three different geometries of nanoparticles—sphere, blade and lamina—are considered. The problem is modeled in the form of momentum, energy and entropy equations. The homotopy analysis method (HAM) is used to find the analytical solution of momentum, energy and entropy equations. The variations of velocity profile, temperature profile, Nusselt number and entropy generation with the influences of physical parameters are discussed in graphical form. The results show that the performance of lamina-shaped nanoparticles is better in temperature distribution, heat transfer and enhancement of the entropy generation.Article Solitons and complexitons to the (2+1)-dimensional Heisenberg ferromagnetic spin chain model(World Scientific Publ Co Pte Ltd, 2019) Aliyu, Aliyu Isa; Li, Yongjin; İnç, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.This paper investigates the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified F-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.Article Numerical Solution of Nonlinear Space-Time Fractional-Order Advection-Reaction-Diffusion Equation(2020) Dwivedi, Kushal Dhar; Rajeev; Das, Subir; Baleanu, DumitruIn this article, a new algorithm is proposed to solve the nonlinear fractional-order one-dimensional solute transport system. The spectral collocation technique is considered with the Fibonacci polynomial as a basis function for the approximation. The Fibonacci polynomial is used to obtain derivative in terms of an operational matrix. The proposed algorithm is actually based on the fact that the terms of the considered problem are approximated through a series expansion of double Fibonacci polynomials and then collocated those on specific points, which provide a system of nonlinear algebraic equations which are solved by using Newton's method. To validate the precision of the proposed method, it is applied to solve three different problems having analytical solutions. The comparison of the results through error analysis is depicted through tables which clearly show the higher accuracy of order of convergence of the proposed method in less central processing unit (CPU) time. The salient feature of the article is the graphical exhibition of the movement of solute concentration for different particular cases due to the presence and absence of reaction term when the proposed scheme is applied to the considered nonlinear fractional-order space-time advection-reaction-diffusion model.Letter Discrete fractional watermark technique(Zhejiang Univ, 2020) Wang, Zai-rong; Shiri, Babak; Baleanu, DumitruThe fractional logistic map holds rich dynamics and is adopted to generate chaotic series. A watermark image is then encrypted and inserted into the original images. Since the encryption image takes the fractional order within (0, 1], it increases the key space and becomes difficult to attack. This study provides a robust watermark method in the protection of the copyright of hardware, images, and other electronic files.Article New numerical approximations for space-time fractional Burgers’ equations via a Legendre spectral-collocation method(Editura ACAD Romane, 2015) Bhrawy, Ali H.; Zaky, Mahmoud A.; Baleanu, DumitruBurgers’ equation is a fundamental partial differential equation in fluid mechanics. This paper reports a new space-time spectral algorithm for obtaining an approximate solution for the space-time fractional Burgers’ equation (FBE) based on spectral shifted Legendre collocation (SLC) method in combination with the shifted Legendre operational matrix of fractional derivatives. The fractional derivatives are described in the Caputo sense. We propose a spectral shifted Legendre collocation method in both temporal and spatial discretizations for the space-time FBE. The main characteristic behind this approach is that it reduces such problem to that of solving a system of nonlinear algebraic equations that can then be solved using Newton’s iterative method. Numerical results with comparisons are given to confirm the reliability of the proposed method for FBE. © 2015, Editura Academiei Romane. All rights reserved.Article On the solutions of a fractional boundary value problem(SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, 2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, KenanThis paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.Article Analytical Approximate Solutions of (N + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations(MDPI AG, 2017) Açan, Ömer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet GiyasIn this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.Article A Result On A Pata-Ciric Type Contraction At A Point(MDPI AG, 2020) Karapınar, Erdal; Fulga, Andreea; Rakoˇcevi´c, VladimirIn this manuscript, we define a new contraction mapping, Pata-Cirictype contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ciric. We proved that in a complete space, each Pata-Cirictype contraction at a point possesses a fixed point. We express an example to illustrate the observed result.