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 Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions(2013) Nyamoradi, Nemat; Baleanu, Dumitru; Bashiri, TaherehWe consider a system of boundary value problems for fractional differential equation given by D-0+(beta)phi(p)(d(0+)(alpha)u)(t) = lambda(1)a(1)(t)f(1)(u(t), v(t)), t is an element of (0, 1), D-0+(beta)phi(P)(D(0+)(alpha)v)(t) - lambda(2)a(2)(t)f(2)(u(t), v(t)), t is an element of (0, 1), where 1 < alpha, beta <= 2, 2 < alpha + beta <= 4, lambda(1), lambda(2) are eigenvalues, subject either to the boundary conditions D(0+)(alpha)u(0) = D(0+)(alpha)u(1) = 0, u(0) = 0, D(0+)(alpha)u(1) - Sigma(m-2)(i=1)a(1i) D(0+)(beta 1)u(xi(1i)) = 0, D(0+)(alpha)v(0) = D(0+)(alpha)v(1) =0, v(0) = 0, D(0+)(beta 1)v(1) - Sigma(m-2)(i=1)a(2i)D(0+)(beta 1)v(xi(2i)) = 0 or D(0+)(alpha)u(0) = D(0+)(alpha)u(1) = 0, u(0) = 0, D(0+)(beta 1)u(1) - Sigma(m-2)(i=1)a(1i)D(0+)(beta 1)u(xi(1i)) = psi(1)(u), D(0+)(alpha)v(0) = D(0+)(alpha)v(1) = 0, v(0) = 0, D(0+)(beta 1)v(1) - Sigma(m-2)(i=1)a(2i) D(0+)(beta 1)v(xi(2i)) = psi(2)(v) where 0 < beta(1) < 1, alpha - beta(1) - 1 > 0 and psi(1), psi(2) : C([0, 1]) -> [0, infinity) are continuous functions. The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems. As an application, an example is given to demonstrate some of main results.Article On the existence of solution for fractional differential equations of order 3< δ1≤4(2015) Baleanu, Dumitru; Agarwal, Ravi P; Khan, Hasib; Khan, Rahmat Ali; Jafari, HosseinIn this paper, we deal with a fractional differential equation of order δ1∈(3,4] with initial and boundary conditions, (Formula Presented), addressing the existence of a positive solution (EPS), where the fractional derivatives Dδ1, Dα1 are in the Riemann-Liouville sense of the order δ1, α1, respectively. The function (Formula Presented). To this aim, we establish an equivalent integral form of the problem with the help of a Green’s function. We also investigate the properties of the Green’s function in the paper which we utilize in our main result for the EPS of the problem. Results for the existence of solutions are obtained with the help of some classical results.Article New Estimates of q1q2 -Ostrowski-Type Inequalities within a Class of n -Polynomial Prevexity of Functions(2020) Kalsoom, Humaira; Idrees, Muhammad; Baleanu, Dumitru; Chu, Yu-MingIn this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called n-polynomial preinvex functions. We use the n-polynomial preinvex functions to develop q1q2-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for q1q2-differentiable function. However, the problem has been proven to utilize the obtained identity, we give q1q2-analogues of the Ostrowski-type integrals inequalities which are connected with the n-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.Article New analytical wave structures for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications(2019) Lu, D.; Tariq, K.U.; Osman, M.S.; Baleanu, Dumitru; Younis M., Younis M; Khater, M.M.A.Different types of soliton wave solutions for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq equations are investigated via the solitary wave ansatz method. These solutions are classified into three categories, namely solitary wave, shock wave, and singular wave solutions. The corresponding integrability criteria, termed as constraint conditions, obviously arise from the study. Moreover, the influences of the free parameters and interaction properties in these solutions are discussed graphically for physical interests and possible applicationsArticle New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-MingIn the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (α, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.Article 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 Single and combined optical solitons, and conservation laws in (2+1)-dimensions with Kundu-Mukherjee-Naskar equation(2020) Aliyu, Aliyu Isa; Li, Yongjin; Baleanu, DumitruIn this work, the celebrated (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation (KMNE) proposed to govern the soliton dynamics in (2 + 1)-dimensions along excited resonant wave guides that is doped with Erbium atoms is studied with the aid of ansatz approach and sine-Gordon expansion method (SGEM). The integration algorithms revealed both single and combined optical solitons of the model. These solitons are reported as bright, dark, combined dark-bright and singular solitons. The combined dark-bright and combined singular soliton solutions of the KMNE are to the best of our knowledge reported for the first time in this paper. These solutions supplements the existing ones in the literature. Additionally, we studied the conservation laws (Cls) of the equation by applying the multipliers approach and report the non-trivial fluxes associated with the equation. 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 Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, ShahramBy using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.