Matematik Bölümü Yayın Koleksiyonu

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

Browse

Filters

2005 - 200952010 - 2019132020 - 202412

Settings

Access Right: Closed AccessPublisher: search.filters.publisher.Taylor & Francis Ltd

Search Results

Now showing 1 - 10 of 30
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    On the Characteristic Functions and Dirchlet-Integrable Solutions of Singular Left-Definite Hamiltonian Systems
    (Taylor & Francis Ltd, 2024) Ugurlu, Ekin; Bairamov, Elgiz; Tas, Kenan
    In this work, a singular left-definite Hamiltonian system is considered and the characteristic-matrix theory for this Hamiltonian system is constructed. Using the results of this theory we introduce a lower bound for the number of Dirichlet-integrable solutions. Moreover we share a relation between the kernel of the solution of the nonhomogeneous boundary value problem and the characteristic-matrix.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 9
    Applications of the Novel Diamond Alpha Hardy-Copson Type Dynamic Inequalities To Half Linear Difference Equations
    (Taylor & Francis Ltd, 2022) Kaymakcalan, Billur; Kayar, Zeynep
    This paper is devoted to novel diamond alpha Hardy-Copson type dynamic inequalities, which are zeta < 0 complements of the classical ones obtained fort zeta > 1, and their applications to difference equations. We obtain two kinds of diamond alpha Hardy-Copson type inequalities for zeta < 0, one of which is mixed type and established by the convex linear combinations of the related delta and nabla inequalities while the other one is new and is obtained by using time scale calculus rather than algebra. In contrast to the works existing in the literature, these complements are derived by preserving the directions of the classical inequalities. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities obtained for zeta < 0 into one diamond alpha Hardy-Copson type inequalities and offer new types of diamond alpha Hardy-Copson type inequalities which have the same directions as the classical ones and can be considered as complementary inequalities. Moreover the application of these inequalities in the oscillation theory of half linear difference equations provides several nonoscillation criteria for such equations.
  • Article
    Citation - WoS: 43
    Citation - Scopus: 45
    An Exact Solution of a Casson Fluid Flow Induced by Dust Particles With Hybrid Nanofluid Over a Stretching Sheet Subject To Lorentz Forces
    (Taylor & Francis Ltd, 2022) Mebarek-Oudina, Fateh; Zaib, Aurang; Ishak, Anuar; Abu Bakar, Sakhinah; Sherif, El-Sayed M.; Baleanu, Dumitru; Khan, Umair
    The concept of a hybrid nanofluid has piqued the interest of numerous researchers due to its potential for increased thermal properties, which results in high transfer rates. Hybrid nanofluids are used in heat transport systems such as electronic cooling, and applications in biomedical and pharmaceutical relief. Thus, the present paper inspects the impact of Lorentz forces on the Casson fluid flow of water-based Fe3O4-MWCNT hybrid nanofluid induced by dust particles from a stretching sheet. The leading PDEs are changed into ODEs by employing similarity variables and then achieving an exact solution for these transformed ODEs. The impacts of distinct physical constraints including fluid interaction particle parameter, Casson parameter, and magnetic parameter on the dust velocity and fluid velocity for normal nanofluid (Fe3O4/H2O) and hybrid nanofluid (Fe3O4-MWCNT/ H2O) are addressed in detail. The present analytic solution shows a strong correlation with earlier published numerical studies in limited cases.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 11
    A Novel Radial Basis Procedure for the Sirc Epidemic Delay Differential Model
    (Taylor & Francis Ltd, 2023) Baleanu, Dumitru; Mallawi, Fouad Othman; Ullah, Malik Zaka; Sabir, Zulqurnain
    The purpose of this work is to construct a reliable stochastic framework for solving the SIRC delay differential epidemic system, i.e. SIRC-DDES that is based on the coronavirus dynamics. The design of radial basis (RB) transfer function with the optimization of Bayesian regularization neural network (RB-BRNN) is presented to solve the SIRC-DDES. The SIRC-DDES is classified into susceptible $ S(x) $ S(x), infected $ I(x) $ I(x), recovered $ R(x) $ R(x) and cross-immune $ C(x) $ C(x). The exactness of the RB-BRNN is performed for three cases of SIRC-DDES by using the performances of the obtained and reference results. The mean square error is reduced by using the training, testing and substantiation performances with the reference solutions. The small values of the absolute error around 10-07 to 10-08 and different statistical operator performances based on the error histogram values, transitions of state investigations, correlation and regression tests also approve the accuracy of the proposed technique.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    A New Insight To the Hamiltonian Systems With a Finite Number of Spectral Parameters
    (Taylor & Francis Ltd, 2023) Ugurlu, Ekin
    In this article, we introduce a new first-order differential equation containing a finite number of spectral parameters and some results on the solutions of this equation. In particular, with the aid of the nested-circles approach we share a lower bound for the number of linearly independent square-integrable solutions of the equation. We share some limit-point criterias. Moreover, we show that some known and unknown scalar and matrix differential equations can be embedded into this new first-order equation. Using the obtained results we present some additional results for some system of scalar multiparameter differential equations. Finally, we share some relations between the characteristic function of a regular boundary-value problem and the kernel of related integral operator.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 22
    A High-Order Unconditionally Stable Numerical Method for a Class of Multi-Term Time-Fractional Diffusion Equation Arising in the Solute Transport Models
    (Taylor & Francis Ltd, 2023) Khan, Arshad; Baleanu, Dumitru; Alam, Mohammad Prawesh
    In this paper, we study a high-order unconditionally stable numerical method to approximate the class of multi-term time-fractional diffusion equations. This type of problem appears in the modelling of transport of certain quantities such as heat, mass, energy, solutes in ground water and soils. The multi-term time-fractional derivative is approximated by using the Crank-Nicolson method for the Caputo's time derivative. The space derivative is approximated by using the collocation method based on quintic B-spline basis functions. We have established the stability and convergence analysis of the proposed numerical scheme thoroughly, and it is shown that the order of convergence in space variable is almost four and in the time variable is O (Delta t(2-max{gamma,gamma i})). To prove the accuracy and efficiency of the developed method, we consider four numerical examples and perform the numerical simulation. The developed algorithm works well andvalidate the theoretical results. The developed method is fourth-order convergent in the space variable, which is almost two orders of magnitude higher than the other spline collocation methods.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 32
    Dark-Bright Optical Solitary Waves and Modulation Instability Analysis With (2+1)-Dimensional Cubic-Quintic Nonlinear Schrodinger Equation
    (Taylor & Francis Ltd, 2019) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
    This paper addresses the (2+1)-dimensional cubic-quintic nonlinear Schrodinger equation (CQNLS) that serves as the model to study the light propagation through nonlinear optical media and non-Kerr crystals. A dark-bright optical solitary wave solution of this equation is retrieved by adopting the complex envelope function ansatz. This type of solitary wave describes the properties of bright and dark optical solitary waves in the same expression. The integration naturally lead to a constraint condition placed on the solitary wave parameters which must hold for the solitary waves to exist. Additionally, the modulation instability (MI) analysis of the model is studied based on the standard linear stability analysis and the MI gain spectrum is got. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CQNLS.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    On the Non-Commutative Neutrix Product of the Distributions X<sup>-r</Sup>+ Ln<sup>p</Sup> X+ and X<sup>μ</Sup>+ln<sup>q< X+
    (Taylor & Francis Ltd, 2006) Tas, Kenan; Fisher, Brian
    Let f and g be distributions and g(n) = (g*delta(n))(x), where delta(n)(x ) is a certain sequence converging to the Dirac delta-function. The non-commutative neutrix product f o g of f and g is defined to be the neutrix limit of the sequence {fg(n) }, provided its limit h exists in the sense that [GRAPHICS] for all functions phi in D. It is proved that (x(+)(-r) ln(p) x(+)) o (x(+)(mu) ln(q) x(+)) = x(+)(-r+mu) ln(p+q) x(+) (x(-)(-r) ln(p) (x)-) o (x(-)(mu) ln(q) x(-)) = x(-)(-r+mu) ln(p+q) x(-) for mu < r - 1;mu not equal 0, +/- 1, +/- 2,..., r = 1,2,..., and p, q = 0, 1, 2,....
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation
    (Taylor & Francis Ltd, 2021) Erhan, Inci M.; Fulga, Andreea; Karapinar, Erdal; Aksoy, Umit
    In this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 6
    On a Problem for the Nonlinear Diffusion Equation With Conformable Time Derivative
    (Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Zhou, Yong; Huu Can, Nguyen; Au, Vo Van
    In this paper, we study a nonlinear diffusion equation with conformable derivative: D-t((alpha)) u = Delta u = L(x, t; u(x, t)), where 0 < alpha < 1, (x, t) is an element of Omega x (0, T). We consider both of the problems: Initial value problem: the solution contains the integral I = integral(t)(0) tau(gamma) d tau (critical as gamma <= -1). Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data). For the initial value problem, the lack of convergence of the integral I, for gamma <= -1. The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.